IB Physics Glossary



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A

Absolute magnitude

M, is a measure of how bright an object appears or the apparent magnitude, when it is observed from a distance of 10 pc. (d).

Absorbed dose

D, is the amount of energy absorbed by a unit mass of material or body tissue where D = absorbed energy/mass. Its units are Jkg-1 or the Gray (Gy).

Acceleration

is the rate of change of velocity. (d.)
a=\frac{\Delta v}{\Delta t} = \frac{v-u}{t} .

Accommodation

is the process by which the lens in the eye can focus on both near and far objects. When we focus on distant objects the lens is longer and thinner due to the effect of the cilary muscles and the taut fibers. When we focus on nearby objects the lens becomes shorter and thicker due to contraction of the ciliary muscles.

Accuracy

tells us how close the measured value of a quantity is to its true value. An accurate measurement is "close" to a true value. An inaccurate measurement is "far" from a true value.

Acoustic impedance

of a substance is the product of medium density, \rho, and speed of sound waves, c, in the medium Z= \rho \times c. Its unit is kgm-2s-1. Impedance matching occurs when the impedance of two media are equal. The incident waves are transmitted (100%) through the media. When there is a large difference in impedance between media most of the incident sound waves are reflected.

Adiabatic process

occurs without any energy transfer to or from the gas.

adiabatic

A rapid expansion or compression is approximately adiabatic since \Delta Q \approx 0.

The 1st law of thermodynamics
Q = \Delta U + W
becomes
0 = \Delta U + W
or
\Delta U = - W.

An adiabatic expansion, W > 0 \Rightarrow U < 0, is a cooling process.

An adiabatic compression, W < 0 \Rightarrow U > 0, is a heating process.

Albedo

is the ratio of total solar energy reflected back from Earth into space to the total incident solar energy. (d)

Alpha decay

^A_ZX \rightarrow~{}^{A-4}_{Z-2}Y + ^{4}_{2}\alpha

or

^A_ZX \rightarrow~{}^{A-4}_{Z-2}Y + ^{4}_{2}He.

Where X is the parent nucleus, Y is the daughter nucleus, A is the number of nucleons and Z is the number of protons.
An example decay is
^{241}_{95}Am \rightarrow~{}^{237}_{93}Np + ^{4}_{2}\alpha.

Properties of alpha particles include
  • discrete energy spectrum
  • +2 charge
  • relatively heavy
  • strongly ionizing
  • short range in air (cm)/low penetration
  • can be blocked by a sheet of paper
  • deflected by magnetic-fields and electric-fields (in direction opposite to beta particles)


Ammeter

measures current flowing through a component. It is placed in series with the component. An ideal ammeter has zero resistance so that it has no effect on the current flowing.

Ampere

is the SI unit of electrical current and is defined through the magnetic force acting between two parallel wires. If the magnetic force between two wires separated by 1m, each of length 1m, carrying equal currents, equals 2 x 10-7 N, then the current in each wire equals 1 Ampere.

Anti-node

a region of maximum wave displacement. Amplitude 2A.

Apparent brightness

the energy from a star per second incident on 1m2 of the Earth's surface.(d)

Apparent magnitude

a measure of the brightness of a star as it appears from Earth. (d).

Astronomical Unit

is the average distance between Earth and Sun. (s)

Attenuation

is the drop in intensity as X-rays pass through a medium.

Attenuation coefficient

µ, is a constant for a material at a given X-ray energy which allows us to calculate X-ray intensity, I, given any thickness of material x and incident X-ray intensity I0 where I = I_0 e^{-\mu x}.

Atwood's Machine

is a pulley system with a difference in mass between the two sides of the pulley:
atwood

The acceleration of the pulley, from Newton's 2nd law, is given by

a = g \times \frac{m-}{m+}
where

m- is the mass difference m2-m1, and m+ is the sum of the masses m1+m2.

Audiogram

is a record of the variation of hearing with frequency for a patient.

Avogadro's constant

is the number of atoms in 12g of Carbon-12 (6.02x1023). (d)

B

Bacquerel

, Bq, is the SI unit of activity for radioactive sources. It is equivalent to a count or disintegration per second. The activity is measured, typically, with a Geiger-Muller (GM) tube.

Beta decay

^A_ZX \rightarrow~{}^{A}_{Z+1}Y + ^{0}_{-1}\beta + ^{0}_{0}\bar{\nu}

or

^A_ZX \rightarrow~{}^{A}_{Z+1}Y + ^{0}_{-1}e + ^{0}_{0}\bar{\nu}.

Where X is the parent nucleus, Y is the daughter nucleus, A is the number of nucleons and Z is the number of protons.
An example decay is
^{90}_{38}Sr \rightarrow~{}^{90}_{39}Y + ^{0}_{-1}\beta + ^{0}_{0}\bar{\nu}.

Properties of beta particles include
  • continuous energy spectrum
  • -1 charge
  • relatively light
  • moderately ionizing
  • moderate range in air (cm to m)/medium penetration
  • can be blocked by a few mm of aluminum or thin lead sheets
  • deflected by magnetic-fields and electric-fields (in direction opposite to alpha particles)

More info



Binary to decimal conversion

for a five bit-number
b_4 b_3 b_2 b_1 b_0

the decimal equivalent is

b_4 \times 2^4 + b_3 \times 2^3 + b_2 \times 2^2 + b_1 \times 2^1 + b_0 \times 2^0.

An example is the binary number 10101 which in decimal is

1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 21.


Binding energy

is the energy required to assemble a nucleus or to separate the nucleus into its individual components/nucleons. (d)

The binding energy per nucleon is the total binding energy for a particular nucleus divided by the number of nucleons contained in the nucleus.

For energy to be released in a nuclear reaction, fusion or fission, the binding energy must increase.

nuc_energy
Image taken from http://www.smsec.com/en/nucl/07_1.htm

Blind spot

is a region where the optical nerve leaves the retina which does not contain rods or cones.

Brewster's law

When the angle of incidence equals Brewster's angle, the reflected and the refracted rays are perpendicular to each other. The reflected ray becomes completely horizontally plane-polarized.

brew

n=\tan \phi

C

Capacitance

is the ratio of charge to potential difference or voltage,

C=\frac{Q}{V}.

Its units are Farads.

CCD

is a charged coupled device such that the amount of charge that builds up on one of its pixels is proportional to the light intensity falling on the pixel.
The photoelectric effect is responsible for conversion of photons energy to electron energy.

CCD resolution

is possible if the size of an image covers at least two pixels.

CD/DVD pit depth

is given by d = \frac{\lambda}{4}where \lambda is the wavelength of the laser for the CD/DVD reader.The distance corresponds to a total additional distance of \frac{\lambda}{2} travelled by the laser light at a pit-land interface (corresponding to binary 1).
DVDs (shorter pit length and double layers) have about 7 times the storage capacity of CDs. Changing or reducing the laser wavelength can increase the resolution, by decreasing \theta= 1.22 \frac{\lambda}{b}, thus allowing more pits and therefore greater storage capacity. Bluray technology uses shorter wavelength laser light.

Chandrasekhar core limit

equals 1.4 solar masses for the core of a (super) red giant.

Low mass stars: core mass < 1.4 solar masses
Red giant -> Planetary nebula -> White dwarf
Helium burns and fuses in the core into carbon and oxygen.

High mass stars: core mass > 1.4 solar masses
Super Red Giant -> Supernova -> Neutron star or Black Hole
Silicon burns and fuses in the core into iron.

Circular motion

occurs under the following conditions:
  • the force F, and therefore acceleration a, and change in velocity \Delta v, is directed towards the center of a circle;
  • the velocity is perpendicular to the force, v \perp F.

Data booklet reference:

\nu \; = \;\omega r
a\; = \;{{{v^2}} \over r}\; = \;{{4{\pi ^2}r} \over {{T^2}}}
F\; = \;{{m{v^2}} \over r}\; = \;m{\omega ^2}r

Coefiicient of voume expansion

\gamma, is the fractional change in volume of a substance \frac{\Delta V}{V} per unit degree change in temperature \Delta T:
\gamma = \frac{\Delta V}{V \times \Delta T}=\frac{V_2-V_1}{V_1 \times (T_2-T_1)}.
The SI unit is K-1.

For problems involving rise in sea level
  • height, h, of water can be found from
h = \frac{Volume}{Area}
  • rise is seal level can be calculated using
\Delta h = \gamma \times h \times \Delta T.

Comets

have
a. highly elliptical orbits;
b. large orbital radii beyond planets;
c. orbit are in many different planes. (d)

Conductive hearing loss

occurs when the air conduction thresholds (middle ear) show a hearing loss but the bone conduction thresholds (cochlea) are normal. Reasons include
  1. blockages - build up of wax of fluid;
  2. accidents - damaged middle ear or ruptured eardrum;
  3. diseases/infection - middle ear bones are prevented from moving;
  4. age - bones in middle ear become solidified with age.

Conductor

A material that allows the flow of electric charge through it.
Conduction is the flow of charge (free electrons) from atom to atom within a material.

Constellation

is a pattern of stars, as seen from Earth, which are not close to one another in space. (d)

Constructive interference

occurs when two waves meet such that the resultant wave displacement is greater than that of the individual waves with path difference = n \times \lambda or phase difference = n \times 2\pi. (s)

Coulomb's Law

F =\left( \frac{1}{4 \pi \epsilon_0}\right) \frac{q_1 q_2}{r^2} = k \frac{q_1 q_2}{r^2}
where F is the force exerted by particle 1 on particle 2 (and vice versa), k is the Coulomb/electric constant, 8.99 x 109 Nm2C-2, q1 is the charge of particle 1, q2 is the charge of particle 2 and r is the distance between the centres of the particles/charges.

Note k=\frac{1}{4 \pi \epsilon_0}, where \epsilon_0=8.85×10−12 C2 N−1m−2 is the permittivity of free space. We usually just use k.


We assume the charges are point-like and all the charge is concentrated in the center. An approximation is to assume the separation of the charges, r, is much greater than their radii.

The law is an inverse-square-law, F \propto \frac{1}{r^2}.

Critical density

is the density which produces a flat universe. In a flat universe the rate of expansion of the universe gradually slows down, asymptotically approaching a zero rate of expansion. (d)

D

Damping

involves a force that is always in the opposite direction to the direction of motion of the oscillating particle/system and the force is a dissapative force which reduces the total energy of the system. (d)


damping


Also

\frac{E_{n+1}}{E_n}=\(\frac{A_{n+1}}{A_n}\)^2

the ratio of successive peak energies equals the ratio of successive amplitudes squared. For example, in the case below, the amplitude falls from 4.3 cm to 2.7 cm. Remaining energy is (2.7/4.3)2 = 0.394 or 39.4%.

damping_2

de Broglie wavelength

is given by
\lambda = \frac{h}{p}.

where h is Planck's constant, and p is the momentum of a particle.

Since waves behave like particles, de Broglie suggested particles can behave like waves with wavelength λ.

The formula, since p = m v, and EK = p2/2m, can be written as

\lambda = \frac{h}{p}=\frac{h}{mv}=\frac{h}{\sqrt{2mE_K}}=\frac{h}{\sqrt{2 m e V}},

where v is the velocity of the particle, EK is the kinetic energy, and V is the potential difference that can accelerate a charged particle.

Decay constant

\lambda, is the probability of a radioactive decay per unit time.

N=N_0e^{-\lambda t}
at t=t1/2, N=N0/2: after one half-life the number of nuclei halves
=>
\frac{N_0}{2}=N_0e^{\lambda t_{1/2}}
=>
\frac{1}{2}=e^{-\lambda t_{1/2}}
or
 2=e^{\lambda t_{\frac{1}{2}}}
=>
\ln 2=\lambda t_{1/2}
or
t_{1/2} = \frac{\ln 2}{\lambda}.

A shorter half-life indicates a more active sample or a higher value for the decay constant (greater probability for a decay).

A a short half-life sample can be measured from the activity-time graph, simply finding the time for the activity to fall by a factor of 2.

For a long half-life sample, the activity, A, is measured at the same time as the mass, m, of the sample. We know 
number of atoms, N = number of moles, n, times Avogadro's constant, NA
and number of moles, n = mass in grams, m/atomic mass number, a, therefore

N = \frac{m}{a} \times N_A

Since 

A = \lambda N then \lambda = \frac{A}{N}

We can find a value for \lambda and t_{1/2}.

decimal to binary conversion

can be completed by dividing by 2 and keeping track of the remainder: an example is 21

remainder 

21
1 (lsb)10
05
12
01
1 (msb)0

which gives 10101.


Degraded energy

is transformed energy which is no longer available to perform useful work. (d)

Derived units

are not fundamental but can be expressed in terms of fundamental units.

Destructive interference

occurs when two waves meet such that the resultant wave displacement is less than that of the individual waves: path difference = (n+ \frac{1}{2}) \times \lambda or phase difference = (2n + 1) \times \pi.

Displacement

is the linear distance of the position of an object from a given reference point. (d.)
s=\Delta x=x_2-x_1.

Doppler effect

is the apparent change in the frequency of a wave source due to the relative motion between the wave source and observer.

Let f^\prime = observed frequency
f = actual wave frequency
v = speed/velocity of waves in medium (fixed by medium and its properties)
u_s = speed/velocity of wave source
u_0 = speed/velocity of observer

For a moving source - stationary observer
(change in observed wavelength of source)

f^\prime = f \left(\frac{v}{v\pm u_s}\right)

Use \pm \rightarrow -, f^\prime > f, \lambda^\prime < \lambda (decrease in wavelength), if wave source moves towards observer

Use \pm \rightarrow +, f^\prime < f, \lambda^\prime > \lambda (increase in wavelength), if wave source moves away from observer


For a moving observer - stationary source
(change in relative speed of waves)

f^\prime = f \left(\frac{v \pm u_0}{v}\right)

Use \pm \rightarrow +, f^\prime > f, increase in relative speed/velocity of waves (v + u_0), if observer moves towards wave source.

Use \pm \rightarrow -, f^\prime < f, decrease in relative speed/velocity of waves (v - u_0), if observer moves away from wave source.

For electromagnetic waves

\Delta f = \frac{v}{c} f

where v is the speed of the wave source and c is the speed of electromagnetic waves in a vacuum.

Doppler flow-speed measurements

can be used to determine the speed of moving objects such as that of
  • a car with a speed "gun"
  • blood flow with ultrasound
through

U = v \frac{|f^\prime - f|}{f^\prime + f} = v \frac{f^-}{f^+}

where
f^\prime= measured/shifted frequency
f = actual wave frequency
f^+ = f^\prime + f
f^- = f^\prime - f
v= speed/velocity of waves in medium (fixed by medium and its properties)
U= speed/velocity of moving target source.

Dose equivalent

H, indicates the effective absorbed dose based on the type of ionization radiation being used. H = Q D, where is the quality factor of the ionization.
The units for H is also Jkg-1 (Gy) but we use the Sievert (Sv) to distinguish it from absorbed dose.

E

Eclipsing binary stars

are identified by a periodic dip in their combined brightness-time curve.

Effective half-life

the time taken for the activity of a medical radioactive isotope to reduce by half, taking into account both physical and biological removal of activity from the body such that

\frac{1}{T_E} = \frac{1}{T_P} + \frac{1}{T_B}

or

T_E = \frac{T_P \times T_B} {T_P + T_B}

where TE is the effective half-life, TP is the physical half-life and TB is the biological half-life.

Note the decay constants add:

\lambda_E = \lambda_P + \lambda_B.

Efficiency

is the ratio of useful power of a system to the input power or the ratio of useful energy transformed to the total energy input. (d)

Approximate overall energy efficiencies for different types of power station are Coal: 35%, Gas: 45% & Oil: 38%.

Elastic collisions

occur when the total kinetic energy of a system remains constant.

Electric current

is defined in terms of force per unit length between two parallel current-carrying conductors. (d)

The electric current flowing in a circuit is the rate of flow of charge, I = \frac{\Delta q}{\Delta t}.

Electric field strength

is the force per unit charge exerted on a positive test charge placed in the field.

E = \frac{F}{q}=\frac{k\frac{Qq}{r^2}}{q}=k \frac{Q}{r^2}.

Its unit is NC-1. It is a vector quantity and is always directed from the positive charge (+) to the negative charge (-) and points tangentially (\perp) to the surface of the charge.


efields

Note: 
1. An attractive force
2. A repulsive force (no field lines at centre)
3. Positive point charge to ground
4. Parallel plates (no edge effects) with constant electric field 



uneven

For charges of unequal magnitude, the field lines are shifted towards the lower magnitude charge. The field line pattern is pear-shaped with the "apex" closer to the lower magnitude charge.

The field around a charged conductor

At equilibrium, the charge and electric field follow these guidelines:
  • the excess charge lies only at the surface of the conductor
  • the electric field is zero within the solid part of the conductor
  • the electric field at the surface of the conductor is perpendicular to the surface
  • charge accumulates, and the field is strongest, on pointy parts of the conductor
[source, http://physics.bu.edu/~duffy/py106/Electricfield.html]

For a sphere of radius R the electric field varies with distance r from centre of sphere as shown below.

e_field_sphere








Electric Potential Difference

is the work done per unit charge in moving a small positive charge between two points. (d)

Electrical circuit symbols

cs

Electrical power

can be expressed in three ways

P = V I

P = I^2 R - used for power dissiapation due to heating in the transmission of electricity.

P = \frac{V^2}{R}.

Electronvolt

is the work done in moving an electron through a potential difference of 1 volt. (d)

A charge, q, gains kinetic energy q V when it is accelerated through a potential difference V:

q V = \frac{1}{2}m v^2.

Elevator weight

is used to show how the reaction force, between a person standing in an elevator and the floor of the elevator, varies with up/down acceleration of the elevator:

elevator

Note, the actual weight of the person does not change but an increase or decrease in the reaction force produces a change on the weighing scale in elevator.

Emf

or electromotive force, is the total energy supplied by a cell/battery per unit charge as it flows through the cell/battery. (d)

Emissitivity

is the ratio of power emitted (per unit area) by a body to the power emitted (per unit area) by a black body of the same dimensions at the same temperature
or

the ratio of power emitted by a body to the power emitted if it were a black body. (d)

Energy density

is the energy liberated per unit mass of fuel consumed. Its unit is Jkg-1.(d)

Entropy

is a system property that expresses the degree of disorder in the system. 

Equilibrium position

is the position where a particle would remain at rest if not disturbed. (d)

Escape velocity

is the velocity that an object needs at the surface of the planet with sufficient kinetic energy to escape the gravitational attraction of the planet.
v_{esc} = \sqrt{\frac{2GM}{R}} = \sqrt{2Rg}
where G is the universal gravitational constant, M is the mass of the planet, R is the radius of the planet and g is the acceleration due to gravity.

For a Black Hole, the escape velocity equals c, the velocity of light in empty space. The above equation becomes
c= \sqrt{\frac{2GM}{R}}
and
R= R_s = \frac{2GM}{c^2}
where Rs is the Schwarzchild radius.

Explosive collisions

occur when the total kinetic energy of a system increases.

F

Far point

is the most distant point from the eye for which the eye can focus on (assumed to be \infty).

Faraday's law

states, the induced emf is proportional to the rate of change of magnetic flux linkage:

\epsilon \propto \frac{\Delta \Phi}{\Delta t}.

First law of thermodynamics

states, Q = \Delta U + W.
Where
Q is the heat supplied to system, \Delta U is the change in the internal energy, W is the work done by gas, all in Joules. It is the law of conservation of energy.

Note
a. Q > 0, heat in; Q < 0, heat out

b. \Delta U > 0, \Delta T > 0; \Delta U < 0, \Delta T < 0

c. W > 0
, work done by gas; W < 0, work done on gas.

Force field

is a region of space where masses/charges feel a force.

Forced oscillations

occur when an object is forced to oscillate by a periodic external force. (d)

Fuel enrichment

Enrichment is the process by which the isotopic composition of a nuclear fuel is increased to make nuclear fissions more likely. Typically, uranium fuel rods are enriched, via neutron bombardment, to ensure that the percentage content of uranium-235 is increased.

Fundamental units

are the most basic units which cannot be expressed in terms of other units. The seven fundamental units are
1. meter (m);
2. second (s);
3. kilogram (kg);
4. Kelvin (K);
5. The Ampere (A);
6. mole (mol);
7. candela (cd).

G

g versus E




GravitationalElectric
ForceF = G \frac{m_1 m_2}{r^2}F = k \frac{q_1 q_2}{r^2}
Constant

G k
Field strength
g = \frac{F}{m} = G \frac{M}{r^2}

F = m g
E = \frac{F}{q} = G \frac{Q}{r^2}

F = q E
Other detailsForce is always attractiveForce can be attractive (for like charges) or repulsive (for opposite charges)
Acts on particles

with mass

with electric charge

Galactic cluster

is a collection of galaxies grouped together due to the gravitational attraction between them. (d)

Galactic supercluster

is a group of galactic clusters. (d)

Galaxy

is a large group of stars gravitationally bound together (approx. 1010 stars, diameter 105 ly). (d)

Gamma decay

^A_ZX^* \rightarrow~{}^{A}_{Z}X + ^{0}_{0}\gamma


where X* is an excited nucleus, X a de-excited nucleus, A is the number of nucleons and Z is the number of protons. A sample gamma decay is
^{40}_{18}Ar^* \rightarrow~{}^{40}_{18}Ar + ^{0}_{0}\gamma


Properties of gamma particles include
  • discrete energy spectrum
  • zero charge
  • mass-less (but have momentum!)
  • weakly ionizing
  • long range in air (light-years)/high penetration
  • can be blocked by thick lead sheets ( approx. 10 cm)
  • not deflected by magnetic-fields and electric-fields

Gas laws

can be found, for an ideal gas, using the ideal gas equation P V=n R T. Note T is the absolute temperature and its unit is Kelvin (ºC + 273). Typical units: pressure P, Pa of kPa; volume V, m3 .

1. For a fixed temperature of gas (and amount of gas, ie. n fixed)
P V = constant or P \propto \frac{1}{V}.
Pressure is inversely proportional to Volume.

2. For a fixed volume of gas (and amount of gas, ie. n fixed)
 P = constant \times T or P \propto T.
Pressure is proportional to Temperature.

3. For a fixed pressure of gas (and amount of gas, ie. n fixed)
 V = constant \times T or V \propto T.
Volume is proportional to Temperature.


More generally one can write

\frac{P_2 V_2}{P_1 V_1} = \frac{n_2 T_2}{n_1 T_1}.

Gravitation versus Electric Potential

pot_1
pot_2

Gravitational field strength

is the force per unit mass on a small (test) mass at the point. (d)

g = \frac{F}{m}=\frac{G\frac{Mm}{r^2}}{m}=G \frac{M}{r^2}.

Its unit is Nkg-1. It is a vector quantity and is always directed towards the centre of the mass and points tangentially (\perp) to its surface.

g

To compare the gravitational field strength for different masses/planets

\frac{g_x}{g_y}=\frac{M_x}{M_y} \left(\frac{r_y}{r_x}\right)^2.

Greenhouse effect

The atmosphere is transparent to many frequencies of electromagnetic radiation. Much of the power received from the Sun is in the visible and ultraviolet regions. This causes the surface of the Earth to warm up and radiate in the infrared (heat). Some of this infrared radiation is absorbed by gases in the atmosphere, causing the atmosphere to warm up, and re-radiated in all directions. The net effect is that the atmosphere and the surface of the Earth are warmed.

Greenhouse gases

are gases in the atmosphere that absorb infrared radiation. The principle greenhouse gases are carbon dioxide (CO_2), methane (NH_4), water vapour (H_2O), and nitrous oxide (NO_2). Ozone and chlorofluorocarbons (CFCs) also contribute to the greenhouse effect.

H

Half-life

t_{\frac{1}{2}}, is the time required for the initial activity of a radioactive sample to be reduced by a factor of 2 or the time requird for the initial number of radioactive nuclei to be reduced by a factor of 2. (d)


Half-value thickness

is the length of material through which X-rays must travel to reduce their intensity by 2 where x_{\frac{1} {2}} = \frac{ln 2} {\mu}, where \mu is the attenuation coefficient.

Heat exchanger

allows the nuclear reactions to occur in a place that is sealed off from the rest of the environment. The reactions increase the temperature in the core. This thermal energy is transferred to heat water, and the steam that is produced turns the turbines.

Hubble's law

states the recessional speed, v, of a galaxy is proportional to its distance, r, from the Earth or galaxies move away from each other with a speed proportional to their separation: v \propto r or v=H \times r, where H is Hubble's constant.

Hybrid vehicles

use electric motors with a petrol engine as back-up to provide additional power when necessary. Sophisticated computerized systems switch from the electric motor to the petrol engine and back as required.

I

Ideal gas

is a gas in which the molecules do not interact or the intermolecular forces can be neglected. (d)
The ideal gas equation is PV=nRT. Here we use absolute temperature, T, with unit Kelvin.

Impulse

is the change in momentum or the product of force and time: \Delta p = F \times \Delta t. (d)
Its unit is N s (or kg m s-1).

Inclined plane

is used to show the forces acting on a block which rests, or moves, along the plane:
incline

The component of the weight down the plane is

 m g \sin\theta.


Inelastic collisions

occur when the total kinetic energy of a system decreases.

Insulator

a material that does not allow the flow of electric charge through it.

Internal energy

of a substance is the total potential energy and random kinetic energy of the molecules of the substance. (d)

Internal resistance

of a cell/battery is the effective additional resistance that is added to a circuit by the cell/battery. This is caused by the electrical energy generated by the chemical reactions inside the cell/ battery which is dissipated within the battery when a current flows:

\epsilon = I (R + r),

where \epsilon is the emf of the cell/battery, I is the current flowing through the circuit, R is the resistance of the circuit component(s) and r is the internal resistance of the cell/battery.

A graph of voltage/potential difference across external resistor (y-axis) against current flowing (x-axis) can be used to find
  • the internal resistance, r = - gradient
  • emf of cell/battery, \epsilon= y-intercept

Ionization radiation

is radiation composed of particles that individually carry enough energy to liberate an electron from an atom thus ionizing it.

Taken from wikipedia.

Isobaric process

takes place at constant pressure.

isobaric

The 1st law of thermodynamics is

Q=\Delta U + W, and W=P \Delta V.

Isochoric process

occurs at constant volume.
isochoric



The 1st law of thermodynamics

Q=\Delta U + W
becomes
Q=\Delta U (all heat converted into internal energy)
since
\Delta V = 0 \Rightarrow W = 0 (no work is done by gas).

Isothermal process

occurs at constant temperature.
isothermal

The 1st law of thermodynamics

Q=\Delta U + W
becomes
Q=W (all heat converted to work)
since
\Delta T = 0 \Rightarrow \Delta U = 0.

Isotope

of an element has the same number of protons (charge) but a different number of neutrons (mass). (d)

K

Kepler's 3rd law

of planetary motion states the orbital period squared is proportional to the mean orbital radius cubed:
T^2 \propto r^3.


Derivation

F = G \frac{Mm}{r^2}=\frac{mv^2}{r}.
or
 G \frac{M}{r}=v^2.

Since the speed, v, is the distance travelled in one orbit, 2 \pi r, divided by the orbital period T we can write

 G \frac{M}{r}=(\frac{2 \pi r}{T})^2
or
 G \frac{M}{r}=\frac{4 \pi^2 r^2}{T^2}

then

T^2 = \frac{4 \pi^2}{GM} \times r^3

or

T^2 = constant \times r^3 => T^2 \propto r^3.

Kinetic energy

is the energy of a moving object.

Kinetic theory of gases


is a theory which treats molecules in a gas as mechanical objects. We assume that

1. A gas contains a large number of molecules;

2. Molecules have a range of kinetic energies, and therefore a range of speeds;

3. A gas molecule occupies a volume much less than that of the volume of the gas;

4. Collisions of molecules with other molecules and with the walls of the container are elastic;

5. Molecules exert forces on other molecules or on container walls only when contact occurs;

6. Collisions times are small compared to time between collisions;

7. Molecules obey the laws of Newtonian mechanics;


L

Law of Conservation of Charge

states that the total charge of a closed system is constant.

Law of Conservation of Energy

states, energy cannot be created or destroyed but is converted from one form into another or the total amount of energy in the universe is constant.

Law of conservation of momentum

states, the total momentum of an system remains constant if no external forces act on the system.

Lenz's law

states the direction of the induced emf is such as to tend to oppose the change producing it. (s)

Light-year

ly, is the distance traveled by light in one year in a vacuum or empty space. (d)

Linear momentum

is the product of mass and velocity, p= m v. (d)

Log-log plots

are used to find the value of the exponent n and coefficient a for the general relationship  y= a x^n.
The value of the gradient for the log-log plot equals n and a= log^{-1}{(\text{y-intercept})}.
For example
A linear relationship should have n \approx 1;
A square-root relationship should have n \approx \frac{1}{2};
A quadratic relationship should have value n \approx 2;
An inverse-square relationship should have value n \approx -2.

LSB

least significant bit is the right-most or the trailing bit in a binary number.

Luminosity

is the power radiated or energy radiated per unit time by a star. (d)

M

Magnetic fields

are in the direction from North pole (N) to South Pole (S):

B_1

Like poles repel:
B_3

Unlike poles attract:
B_2


For a straight wire carrying a current I:

rhr
Use the right-hand-screw rule to find the direction of B-field

wire



For a coil carrying a current I:

coil


Looking into the coil

- if direction of current is anti-clockwise then the end of the coil is a North Pole (magnetic field lines exit)
- if direction of current is clockwise then the end of the coil is a South Pole (magnetic field lines enter)


For a solenoid carrying a current I:

solenoid
Looking into the solenoid

- if direction of current is anti-clockwise then the end of the coil is a North Pole (magnetic field lines exit)
- if direction of current is clockwise then the end of the coil is a South Pole (magnetic field lines enter)


Magnetic flux

the product of magnetic flux density and area. (d)

Magnetic flux linkage

the product of magnetic flux and number of turn. (d)

Magnetic force

acts on a moving charge or a current carrying conductor. 

We use Fleming's left-hand-rule to find the direction of the magnetic force, given B and I:
LHR
Note: electron displacement is in the opposite direction to conventional current I. F, B and I are perpendicular to each other.



The magnetic force F acting on a charge q moving with velocity v, making an angle θ with the magnetic field of strength B is given by

F=q v B \sin \theta.

Only moving  charged particles making an angle θ with the magnetic field "feel" the magnetic force, ie. v ≠ 0 and q ≠ 0 and θ ≠ 0.



The magnetic force F acting on a current I flowing through a conductor of length L, making an angle θ with the magnetic field of strength B is given by

F= B I L \sin \theta.

Only current carrying conductors making an angle θ with the magnetic field "feel" the magnetic force, ie. I ≠ 0 and θ ≠ 0.

Magnetic force on parallel wires

carrying electrical currents I can be summarized below.
wires


Magnetic force on wires

carrying electrical currents I can be summarized below.
wires


Magnification

, M, is the ratio image size/object size, or

M=\frac{L^'}{L}=\sqrt{\frac{A^'}{A}}

A represents area, L size/height/length.

Magnitude of magnetic field

is defined as 

B=\frac{F}{I L \sin \theta} 

where B is the magnitude of the magnetic field, F is the magnetic force, I is the current, L is the length of conductor and θ is the angle between the current-carrying conductor and the magnetic field.

or 

B=\frac{F}{q v \sin \theta} 

where B is the magnitude of the magnetic field, F is the magnetic force, q is the charge, v is the velocity, θ is the angle between the path of the charged particle and the magnetic field.

Malus' law

The light transmitted, I, by an analyzer with incident intensity I0, is given by I=I_0 \cos^2 \theta.
malus

  • When the analyzer is parallel to plane of polarization of incident light, then 
\theta=0^{\circ}, 180^{\circ} \text{and }\cos^2\theta=1

maximum light intensity is tranmitted

When the analyzer is perpendicular to plane of polarization of incident light (ie. they are crossed), then 

\theta=90^{\circ}, 270^{\circ} \text{and }\cos^2\theta=0

zero light intensity is transmitted.

Mass

is the amount of matter or substance inside an object.
Its value does not change with the strength of gravity. Identical objects on Earth and on the Moon have identical masses.

Mass defect

is the difference between the mass of the nucleus and the sum of the masses of its individual nucleons. (d)

Molar mass

is the mass of one mole of substance in grams. (d)

MSB

most significant bit in a binary number is the left-most or leading non-zero bit.

N

Natural frequency

is the frequency at which an object will vibrate if disturbed. (d)

Near point

is the closest point to the eye on which the eye can focus.

Newton's first law of motion

an object remains stationary or remains at a constant velocity if there is no resultant force acting on the object. (s)

Newton's Law of Gravitation

F = G \frac{m_1 m_2}{r^2}
where F is the force exerted by object 1 on object 2 (and vice versa), G is the gravitational constant (6.67 x 10-11 Nm2kg-2), m1 is the mass of object 1, m2 is the mass of object 2 and r is the distance between the centres of the objects.

We assume the masses are point-like and all the masses is concentrated in the center. An approximation is to assume the separation of the masses, r, is much greater than their radii.

The law is an inverse-square-law, F \propto \frac{1}{r^2}.

Newton's second law of motion

states, a resultant force acting on a body equals the rate of change of momentum of the body, F=\frac{\Delta p}{\Delta t}=\frac{m\Delta v}{\Delta t} = m \times a. (s)

Newton's third law of motion

when two bodies A and B interact, the force that A exerts on B is equal and opposite to the force that B exerts on A. (s)

Node

a region of zero wave displacement.

Nuclear fission

is a nuclear reaction in which large nuclei are induced to break up into small nuclei and release energy in the process.
An example of nuclear fission
^{1}_{0}n + ^{235}_{92}U -> ^{236}_{92}U -> ^{144}_{56}Ba + ^{89}_{36}Kr + 3 ^{1}_{0}n.

Nuclear fusion

is a nuclear reaction in which small nuclei are induced to join together into larger nuclei and energy is released in the process. Nuclear fusion is the main source of the Sun’s energy. An example of hydrogen fusion: 
^{2}_{1}H + ^{2}_{1}H -> ^{3}_{2}He + ^{1}_{0}n.

Nuclear model

A simple nuclear model of the atom consists of a tiny central nucleus containing all the mass and all the positive charge. The nucleus is made up of protons and neutrons. Negative electrons are kept in orbit around the nucleus as a result of the electrostatic attraction between the electrons and the nucleus. Although this simple model helps explain many atomic properties there are reasons why things cannot be this simple.

Nucleon

is a proton or a neutron. (d)

Nuclide

a type of atom that is characterized by
the constitution of its nucleus / the number of protons and neutrons in the nucleus (d)

O

Ohm's law

states that current is proportional to voltage, at constant temperature, I \prop V. (d)
The graph should be a straight line passing through the origin.
For non-ohmic conductors current is not proportional to voltage, I \cancel{\prop} V. The graph is non-linear. Examples of non-Ohmic conductors include

  • filament light bulbs
as I \uparrow, T \uparrow, R \uparro \Rightarrow gradient is not constant, or, as I \downarrow, T \downarrow, R \downarrow \Rightarrow gradient is not constant.
Typical graphs can be
y-axis: I, x-axis: V, R \uparrow \Rightarrow \frac{V}{I} \uparrow \Rightarrow gradient decreases;

y-axis: V, x-axis: I, R \uparrow \Rightarrow \frac{V}{I} \uparrow \Rightarrow gradient increases.
  • thermistors
NTC (negative temperaure coefficient): T \uparrow \downarrow R \downarrow \uparrow;
PTC (positive temperature coefficent): T \uparrow \downarrow R \uparrow \downarrow.

  • Light dependent resistors (LDRs)
brightness \uparrow \downarrow,  R \downarrow \uparrow;

  • Strain gauge
a variation in strain of a material (deformation per unit length due to the effect of an applied load/mass) produces a variation in electrical resistance of material


One Mole

of substance has as many molecules as there are atoms in 12g of Carbon-12. (d)

Oppenheimer-Volkoff limit

is approximately 2-3 solar masses for mass of core for Super Red Giant;
for core masses < 2-3 solar masses (above 1.4 solar masses) \rightarrow Neutron star
for core masses > 2-3 solar masses \rightarrow Black hole.

Optically active

substances rotate the plane of polarization of the incident light. The amount of rotation may depend on the concentration of the substance/solution and the amount/length/thickness.

active

Orbital Motion

occurs when the gravitation provides the centripetal force for circular orbital motion: F = G \frac{Mm}{r^2}=\frac{mv^2}{r}.

P

Parallel plates

For parallel plates, of separation d, with a potential/voltage difference ΔV across the plates, the electric field, E, is given by 
E=\frac{\Delta V}{d}

The electric field is uniform or constant between the plates.

Examples

plate_1

plate_2



plate_3


plate_4

plate_5

Parsec

is the distance to a star whose parallax angle is 1 arc-second. (d)

Phase difference

\phi, is the difference in phase angle between two oscillations with the same frequency. (d)

Photopic vision

is color vision which occurs at normal light levels. Vision is aided by the three different cone cells, S (for short-wavelengths or blue), M (for medium-wavelengths or green) and L (for long-wavelengths or red).

Polarization

of light occurs when the direction of the electric field oscillations is in the same plane. (d)

Potential divider rule

is used to calculate the potential difference which is shared between components, R1 and R2, placed in series:
pdpd_rule

where R_1 + R_2 is the total resistance and E is the emf.

Note

E=V_{R1}+V_{R2}

for equal resistances, R_1=R_2, the potential difference is shared equally between the resistances

for unequal resistances, R_1 \ne R_2, the potentail difference is not shared equally but will be greater across the resistance with highest value.

Potential energy

is a stored form of energy available to do work.

Power

is the rate at which work is done. (d)

Precision

tells us how consistent repeated measurements are. A precise set of measurements are relatively closer together. An imprecise set of measurements are spread apart.

Pressure

is the force per unit area. (d)

Primary colors

are red, green and blue. Mixed together they produce white.

Principle of Superpostion

when the paths of two waves of the same type coincide, move through each other or cross, the resultant displacement is the sum of the two individual wave displacements at the point. (s)

Progressive travelling wave

transfers energy with no net motion of the medium through which the wave travels. (d)

Projectile motion

  • The vertical and horizontal components of velocity, in a uniform field, are independent of each other.
  • The vertical velocity follows the equations of uniform acceleration. The horizontal velocity, in the absence of air resistance, remains fixed. The velocity, or total velocity, is the vectorial/Pythagorean sum of the horizontal and vertical velocity components since they are perpendicular to each other: V =\sqrt{V_v^2 + V_h^2}.
  • In the absence of air resistance, the range of a projectile is independent of mass of projectile. It depends on the horizontal velocity. The range, D, is the maximum horizontal distance traveled by the projectile: D= V_h \times t.

  • The time of fall is independent of horizontal velocity. It depends vertical height of projectile,  t= \sqrt{\frac{2 \times height}{g}} if projectile has no initial vertical velocity component, ie. it is dropped.

Proportional relationship

y \propto x or y = m x, occurs when the relationship between y and x is linear with a zero y-intercept value, that is, a straight line passing through the origin.
The x- and y-error bars may allow a range of values for the y-intercept, because the lines of max & min gradients, thus showing a possible proportional relationship for a best-fit straight line even if its y-intercept value is non-zero. Beware, for the IB, a best-fit line can be any curve which fits the data points. It does not mean the best-fit straight line.

Pulsar

is a rotating neutron star. (d)

Q

Quality factor

Q, is a measure of the ionization strength of various radioactive source.

Radiation type
Q
\alpha
20
Fast neutrons
10
Slow neutrons
3
Fast protons
1
\beta, \gamma, X-rays
1

Quantum efficieny

is the ratio of emitted electrons to incident photons falling on a pixel.
Increasing the quantum efficiency makes the CCD more sensitive to light.

Quasar

is a quasi-stellar radio source. A compact region in the center of a black hole. (d)

R

Radioactive decay

occurs when a nucleus emits an \alpha-particle/ \beta-particle/ \gamma-particle /ionizing radiations.
The process is random and spontaneous since it is unknown when a nucleus will decay.
The activity is proportional to the number of undecayed nuclei.
The nucleus becomes more (energetically) stable.
There is a constant probability of decay.
The activity/number of unstable nuclei in sample reduces by half over every half-life.
It is not affected by temperature/environmental conditions.

Radioactive decay law

is written as an exponential decay function 
N=N_0 e^{-\lambda t}
N: #nuclei at time t
N0: initial number of nuclei
\lambda: the decay constant - probability of a decay per unit time
t: time 

Note
A = - \frac{dN}{dt}= \lambda N
or
A = A_0 e^{-\lambda t}
where A_0 = \lambda N_0
A: activity at time t
A0: initial activity of sample
\lambda: the decay constant - probability of a decay per unit time
t: time 

Random error

is a fluctuating error often present in experiments. It is linked to precision: imprecise data => "high" random error; precise data => "low" random error. Repeated measurements do reduce random errors. Sources of random errors can include varying reading/human error and other randomly flucuating factors which cannot be controlled during experiments.

Rayleigh Criterion

for images of two wave sources to be just resolved the maximum of one diffraction pattern is coincident with the first minimum of the other. (d)

rc

The minimum anglular separation in the diffraction pattern, \theta_{min} for two objects to be resolved is given by

\theta_{min} = \frac{\lambda}{b}, for single slits of width b;

\theta_{min} = 1.22 \frac{\lambda}{b}, for circular apertures of diameter b.

If two objects at a distance r from the pupil/telescope, separated by distance s, are just resolved then, since s=r \theta, we can write

1.22\frac{\lambda}{b} = \frac{s}{r}

which can be used to solve typical problems on resolution.

Resisitvity

can be found from the resisitivity equation

R = \frac{\rho L}{A},
where R is the resitance, \rho is the resistivity, L is the length and A is the cross-sectional area, A=\pi r^2=\pi \frac{d^2}{4}.

<< Simulation >>


Resistance

is the ratio of voltage to current, R =\frac{V}{I}. (d)

Resistance combinations

occur when resistances or components are placed in series and/or in parallel combinations. The main differences between the two types of combinations are


Series
Parallel
Diagram r1
r2
Current
same current through each resistor
current splits to flow through each resistor; total current through the whole circuit is the sum of the currents through the separate resistors
Potential difference
potential difference is split between the resistors - refer to potential divider rule.
potential difference across each resistor is the same
Resistance
resistance increases, current decreases, when resistors are combined in series
resistance decreases, current increases, when resistors are combined in parallel
Other properties
current has one path to flow through; if one resistor breaks, current stops flowing
current has more than one path to flow through; if one resistor breaks, current can still flow through other resistors
Formulae R =R_1 + R_2 + \ldots + R_n
\frac{1}{R}= \frac{1}{R_1} + \frac{1}{R_2} + \ldots +\frac{1}{R_n}

For pairs this reduces to
R = \frac{R_1 \times R_2}{R_1 + R_2}
ie. product over sum

For identical resistances in parallel, R_1=R_2, R = \frac{R_1}{2}
ie. resistance value halves


Resonance

occurs when an object is forced to vibrate at its natural frequency with a very large increase in amplitude. (d)

Resonance is the opposite to damping.

res_1

If external driving frequency, f, equals to the natural frequency, f0, then
f = f0 or f/f0 = 1, and resonance occurs.
res_2

Notice the resonance amplitude decreases with damping, and the natural frequency decreases.

rms voltage or current

equals \frac{1}{\sqrt 2} times the peak voltage or current. (s)

S

Satellite paradox

occurs when a satellite moves into a low orbit such that the frictional force increases the speed of the satellite.


"As an artificial satellite gradually descends in a near-circular orbit, its linear velocity increases. Its acceleration in the direction of its motion is found to be the same as if the air drag force, reversed, were pushing the satellite.

Scalar multiplication

of vectors, changes the magnitude of the vector but not the direction.
For scalar a and vector \vec{A} with
x- or horizontal component A_H=A \cos \theta
y- or vertical compnonet A_V= A \sin \theta
magnitude A=\sqrt{A_H^2 + A_V^2}

The multiplication a \times \vec{A} has magnitude a \times A.
The division \vec{A} \div a has magnitude A \div a.

Scalar quantities

have magnitude only. Direction or changes in direction have no effect on scalar quantities. Examples include distance, speed, mass and temperature.

Schönberg-Chandrsekhar limit

states, a star leaves the main sequence when it consumes about 12% of its hydrogen fuel. (d)

Schwarzchild radius

is the distance from the centre of a black hole at which the escape velocity is equal to the speed of light in empty space, c. The radius can be found using
R= R_s = \frac{2GM}{c^2}
where G is the gravitational constant, M is the mass of the black hole and c is the velocity of light in empty space.

Scotopic vision

is black and white vision which occurs in low-light conditions. Vision is aided by the rod cells. Cone cells don't play a role.

Second law of thermodynamics

states that

thermal energy cannot spontaneously transfer from a region of low temperature to a region of high temperature

or

the total entropy of the universe must always stay the same or increase.

Secondary colors

are Cyan (Blue & Green), Magenta (Blue & Red) and Yellow (Green and Red).

Sensory hearing loss

occurs when the air conduction thresholds (middle ear) and the bone conduction thresholds (cochlea) both show a hearing losses. If bone conduction losses are greater than a cochlea implant may be required. Reasons include

  1. ageing;
  2. prolonged exposure to excessive noise.

Signifiant figures

a rule, the number of significant digits in a result should not exceed that
of the least precise value upon which it depends.

Simple Harmonic Motion

occurs when the acceleration (or the resultant force) on a body is directed towards equilibrium position and is proportional to its displacement from equilibrium: a \propto -x or F \propto -x. (d)

A typical graph for an object executing SHM is

shm.
Note

1. a = -\omega^2 x;

2. x_0: amplitude/max displacement;

3. v_0= x_0 \times \omega: max velocity;

4. a_0= x_0 \times \omega^2: max acceleration;

5. \omega = \sqrt{\frac{k}{m}}, for a spring-mass system with stiffness k (or force per unit extension) and mass m. From Hooke's law F= -k x = m a.

Snells' law

states, the ratio of the velocities of the waves in two media is equal to the ratio of the sines of the angles of incidence and refraction of the rays: \frac{v_1}{v_2} = \frac{sin \theta_1}{sin \theta_2}.

Sound intensity

is the amount of sound energy falling on a unit area per second.

Sound intensity level (IL)

, or loudness, is the response of the ear to intensity such that
IL = 10 \hspace{3}\log_{10} \(\frac{I}{I_0}\),
I0 = 1.0 x 10-12 Wm-2is the threshold for hearing.

Note to add sound levels, intensities must be used not intensity levels (or loudness) with

I = I_0 \hspace{3}\times \hspace{3} 10^{IL/10}.

Specific Heat Capacity

is the quantity of thermal energy required to raise the temperature of unit mass by one degree. (d)

Specific Latent Heat

is the thermal energy absorbed or released per unit mass of a substance at constant temperature during a change of phase/state. (d)

Spectroscopic binary stars

over time the spectral lines regularly split into two lines and then recombine. As one star approaches observer the other recedes leading to Doppler shifts in opposite directions. When the motion is perpendicular (to the line of sight) there is no wavelength shift;

Speed

is the rate of change of distance. (d.)

Standing Waves vs. Travelling Waves

swsw


Standing Wave
Travelling Wave
sw
tw
Energy
Energy is not transferred by the wave although it does have a wave energy.
Energy is transferred by the wave.
Amplitude
Amplitude varies along the wave. Maximum amplitude is 2A, at anti-node. Amplitude is zero, at node. Amplitude, A, is the same along the wave.
Frequency
All points oscillate with the identical frequency.
All points oscillate with the identical frequency.
Wavelength
Double the distance from adjacent nodes, or adjacent anti-nodes.
Distance between two neighboring successive points which are in phase.
Phase
All points between adjacent nodes are moving in phase.
All points along a wavelength are moving with different phases.

Open-open system

oo

frequency increases in multiples of the fundamental/1st harmonic, f0:
f0, 2f0, 3f0, ... (even & odd multiples)   


Closes-closed system

cc

frequency increases in multiples of the fundamental/1st harmonic, f0:
f0, 2f0, 3f0, ... (even & odd multiples) 


Open-closed system (hybrid)

oc
frequency increases in odd multiples of the fundamental/1st harmonic, f0:
f0, 3f0, 5f0, ..(odd multiples only).
 












Star

a massive body of gas / gas / plasma giving off light / radiant energy / electromagnetic radiation. (d)

Stellar Cluster

is a group of stars bound by gravitation in same region of space. (d)

Surface heat capacity

is the energy required to change the temperature of 1m2 of a planet's surface by 1 degree. (d)

Systematic error

is a constant, "background" error often present in experiments. It is linked to accuracy: inaccurate data => "high" systematic error; accurate data => "low" systematic error. Systematic errors usually shift a the best-fit line up or down maintaining the same gradient. Repeated measurements do not reduce systematic errors. Sources of systematic errors can include mis-calibrated instruments, zero-error on instruments and/or constant human error such as reading-parallax error.

T

Temperature

absolute, is proportional to the average kinetic energy of the molecules of a substance. (d)

The photoelectric effect

is the phenomena by which electrons are emitted from the surface of a metal being illuminated with light/electromagnetic radiation.

When light of different frequencies and different intensities is incident on the surface:

I. There exists a frequency of light (the threshold frequency) below which no electrons are emitted whatever the intensity of the light. Energy is needed to eject the electrons from the surface.

Light in this case is not behaving as a wave but as a particle (photon) since according to the wave model, the energy of a wave depends on its amplitude/intensity so one would expect emission to depend on intensity not frequency.

II. For light above the threshold frequency, the emission of the electrons is instantaneous whatever the intensity of the light.

Light in this case is not behaving as a wave but as a particle (photon) since according to the wave model, energy is delivered continuously to the surface so with a very low intensity wave one would expect the electrons to need a certain amount of time to gain sufficient energy to leave the surface.


E = hf = E_K + \phi

where E = h f is the photon energy, EK is the maximum kinetic energy of the photoelectrons and φ is the work function of the metal.

We can also write

E_K = hf - \phi

or with the Milikan experiment , EK = eVs, where Vs is the stopping potential

eV_s = hf - \phi

or

V_s = (\frac{h}{e})f - (\frac{\phi}{e})

A Vs-f graph yields a straight with gradient = (\frac{h}{e}) and y-intercept=(\frac{\phi}{e}).

Or

V_s = \frac{hc}{e} \times \frac{1}{\lambda} - \frac{\phi}{e}

A Vs-1/λ graph yields a straight with gradient = (\frac{hc}{e}) and y-intercept=(\frac{\phi}{e}).


Notes:

Consider increasing the frequency of light falling on a metallic surface while keeping the light intensity fixed. A greater stopping potential is required to reduce the photo-current to zero. Since the energy per photon increases but the same light intensity should be maintained, the number of actual number of photons, or the photon flux is less, therefore a smaller photo-current flows.

Further reading.




Thermal/Heat Capacity

is the quantity of thermal energy required to raise the temperature of an object by one degree. (d)

Threshold hearing curve

shows that the sound intensity required to be heard is quite different for different frequencies. Most sensitive frequencies (≈ 3kHz) have lower dB values - less sound intensity is required to for the sound to be heard. Least sensitive frequencies have higher dB values - more sound intensity is required for the sound to be heard. Negative dB values indicate sound intensity is below I0, the threshold intensity of hearing. The graph below shows how the curve varies with age: 20, 40 and 60 years.

thc

Threshold intensity of hearing

is the minimum intensity at which sound is heard, I0 = 1 x 10−12 Wm−2.

Tinnitus

is the sensation of ringing in the ears which can be caused by short-term exposure to loud sounds.

Translational equilibrium

occurs when there is no resultant force on an object in any direction:

\Sigma F = 0 which leads to a = 0 \rightarrow \Delta v = 0 \rightarrow v = \text{constant}.

U

Ultrasound A-scan

is an amplitude-modulated scan with information represented as a graph of signal strength against time.

Ultrasound B-scan

is a brightness-modulated scan with information represented as levels of brightness.

Ultrasound choice of frequency

is selected based on
  1. the resolution or size of smallest object being scanned
  2. attenuation which increases with frequency
  3. pulse length.
The best choice of frequency occurs when the organ/object being imaged is about 200 wavelengths from the ultrasound probe:
f = 200 \lambda = 200 \frac{c} {d}
where c is the speed of sound waves in tissue and d is the depth of the organ/object.

Uncertainties

    •    resulting from measurements are combined under the following rules:

addition/subtraction of quantities => add absolute errors

If y = a \pm b \pm c , then \Delta y = \pm (\Delta a + \Delta b+ \Delta c).


multiplication/division of quantities = add relative/fractional/percentage errors

If y = a \times b \times c, then

\frac{\Delta y}{y} = \pm (\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c}), or, \Delta y(\%)= \pm (\Delta a(\%) + \Delta b(\%) + \Delta c(\%))
and
{\Delta y} = \pm y \times (\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c}), or, \Delta y= \pm y \times (\Delta a(\%) + \Delta b(\%) + \Delta c(\%)).

If y = a \div b \div c, then 

\frac{\Delta y}{y} = \pm (\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c}), or, \Delta y(\%)= \pm (\Delta a(\%) + \Delta b(\%) + \Delta c(\%))
and 
{\Delta y} = \pm y \times (\frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c}), or, \Delta y= \pm y \times (\Delta a(\%) + \Delta b(\%) + \Delta c(\%)).

raising quantity to n'th power = multiply relative/fractional/percentage error by n

If y = a^n, then
\frac{\Delta y}{y} = \pm |n| \times \frac{\Delta a}{a}, or, \Delta y(\%)= \pm |n| \times \Delta a(\%)
and 
{\Delta y} = \pm y \times |n| \times \frac{\Delta a}{a}, or, \Delta y= \pm y \times |n| \times \Delta a(\%).

Unified atomic mass unit (u)

is 1/12th the mass of a neutral carbon-12 atom.

Uniform acceleration

occurs when the acceleration a is held constant.
Since acceleration is a vector quantity, constant implies a uniform magnitude and direction for the acceleration. The equations of uniform acceleration are

v=u + at (not given on IB Physics Data Booklet)

s = \frac{u+v}{2} t

s=ut + \frac{1}{2} a t^2

v^2=u^2 + 2 as

where u is the initial velocity, v is the final velocity after time t, a is the acceleration and s is the displacement.

V

Vector addition/subtraction

\vec{A}:
x- or horizontal component A_H=A \cos \theta;
y- or vertical component A_V= A \sin \theta;
magnitude A=\sqrt{A_H^2 + A_V^2};
\tan \theta = \frac{A_V}{A_H}.
\vec{B}:
x- or horizontal component B_H=B \cos \theta;
y- or vertical component B_V= B \sin \theta;
magnitude B=\sqrt{B_H^2 + B_V^2};
tan \theta =\frac{B_V}{B_H}.

Addition
\vec{C} = \vec{A} + \vec{B}:
x- or horizontal component C_H=A_H + B_H;
y- or vertical component C_V= A_V + B_V;
magnitude C=\sqrt{C_H^2 + C_V^2};
tan \theta =\frac{C_V}{C_H}.

Subtraction
\vec{C} = \vec{A} - \vec{B} = \vec{A} + (\vec{-B}):
x- or horizontal component C_H=A_H - B_H;
y- or vertical component C_V= A_V - B_V;
magnitude C=\sqrt{C_H^2 + C_V^2};
tan \theta =\frac{C_V}{C_H}.

Vector quantites

have magnitude and direction. Direction or changes in direction have an effect on vector quantities. Examples include displacement, velocity, acceleration, force, momentum and field strength.

Velocity

is the rate of change of displacement. (d)
v=\frac{\Delta s}{\Delta t}.

Visual binary stars

are stars of a system that are visible as separate stars (with unaided eye or through a telescope/binoculars)

Voltmeter

measures potential difference across a component. It is placed parallel to the component. An ideal voltmeter has infinite resistance so that no current flows through it.

W

Wave amplitude

is the maximum displacement of a particle from its rest/equilibrium position. (d)

Wave displacement

distance of an oscillating particle from its mean/equilibrium position. (d)

Wave frequency

f, is the number of oscillations of the wave source or of a particle per unit time. (d)

Wave intensity

is the rate of flow of energy across a cross-sectional area perpendicular to the direction of wave propagation such that I \propto \text{Wave Amplitude}^2. (d)

Wave period

T, is the time for one complete oscillation/cycle. (d)

Wave speed

v, is the rate at which energy is transferred by the wave or the distance traveled by a wavefront per unit time. (d)
v=\lambda \times f.

Wavelength

\lambda, is the distance moved by a wavefront during one oscillation of the wave source or the distance between consecutive neighboring successive points which are in phase. (d)

Weight

is the force of gravity acting on a mass: W=m g, m is the mass, g is the gravitational field strength \equiv acceleration due to gravity.
Its value does change with the strength of gravity. Identical objects on Earth and on the Moon have different weight values. Its SI unit is the Newton (N).

Work

is force × distance (moved) in the direction of the force. (d)

Work done by a gas

is given by W = P \Delta V.

For an expansion, \Delta V > 0 \Rightarrow W > 0, work is done by the gas.

For a compression, \Delta V < 0 \Rightarrow W < 0, work is done on the gas.


Derivation


Consider a gas in a closed container with a piston of area A in contact with the gas.

1. The gas expands, via some thermodynamic process, and the piston is displaced by \Delta x.
piston

2. The gas does work on the piston (heat is converted into mechanical energy).

3. The work done is W=F \times s, ie. force x displacement:

W = F \Delta x.

4. Recall the pressure exerted by the gas is given by P=\frac{F}{A}, force per unit area. Therefore F = P A.

5. W = F \times s = (P A) \times \Delta x = P (A \Delta x) = P \Delta V, since A \Delta x is the change in volume of the gas.

Work function

\phi, is the minimum energy required to liberate an electron from the surface of a metal:

\phi = h f_0

where f0is the minimum or threshold frequency required to produce the photoelectric effect.



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