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Revision Notes Unit 5 Physics

Physics Unit 5 Revision
Siobhan Parish
Chapter 9
Discovery of the nucleus
Rutherford’s experiment
1. Alpha particles had the same speed as otherwise
slow α particles would be deflected more than the
faster ones on the same initial path
2. Container must be evacuated or
α would be stopped by air α source
3. Alpha source must have a long
half-life or later readings would
be lower than earlier ones due to
radioactive decay
Discovery of the nucleus
Rutherford found:
• Most α particles went through the foil
• ~ 1 in 2000 were deflected
• ~ 1 in 10000 were deflected more than 90◦
Rutherford concluded:
• Nucleus at the centre of the atom contained
most of its mass
• Nucleus was very small
• Nucleus is positively charged
The discovery of the nucleus
• The greater deflection is because the
electrostatic force of repulsion between the alpha
particle and the nucleus increases with
decreased separation between them
• The smaller deflection means the alpha particle
is further away from the nucleus
Discovery of the nucleus
size of the nucleus
• 1 in 10000 α particles scattered >90˚for n layers
of atoms in the foil, (n≈104). Therefore there’s a 1
in 10000n chance of deflection
• Chance = =
•= =
•  d = = ≈ 10-15
Properties of radiation
• Marie Curie discovered the nature of radioactive
• Showed how radioactive compounds could be
separated and identified
• Henri Becquerel discovered that uranium could be
used to produce X-Ray images- saw that it could
penetrate paper and blacken photographic film
• Marie found radium to be >1,000,000 more
radioactive than uranium
Mag field into
α (+ charged)
Properties of radiation
γ (uncharged)
β (- charged)
Rutherford found that radiation:
• Ionised air making it conduct electricity- made a
detector which could measure the radiation from
its ionising effect
• Was of two types: alpha (easily absorbed) and
beta (more penetrating). A third type, gamma, is
even more penetrating and was discovered a
year later
Properties of radiation
• The chamber contains air at atmospheric
• Ions created in the chamber are attracted to the
oppositely charged electrode where they
are discharged
• Electrons pass through the pA as a Ionisation
result of ionisation in the chamber
• Current proportional to the number Insulator
of ions per second
Properties of radiation
• α radiation causes strong ionisation. If the source
is moved away from the top of the chamber
ionisation ceases beyond a certain distance
because α radiation has a range in air of no more
than a few centimetres
• β radiation has a weaker ionising effect than α.
Range in air is up to a metre or more. Produces
fewer ions per mm along it’s path
• γ radiation has the weakest ionising effect,
because photons carry no charge
Properties of radiation
Cloud chambers
• Contains air saturated with a vapour at a very
low temperature
• Due to ionisation alpha and beta particles going
through the cloud chamber leave visible tracks of
minute condensed vapour droplets
• Air space is supersaturated
• The ions produced trigger the formation of
Properties of radiation
• Alpha particles produce straight tracks that radiate
from the source and are easily visible
• Tracks from a given isotope are all of the same
length showing alpha particles have the same
• Beta particles produce wispy tracks that are easily
deflected as a result of collisions with air
• Tracks are not as easily seen as alpha tracks as
beta particles are less ionising
Properties of radiation
• A Geiger tube and counter can be used to test
absorption by different materials
• Each particle of radiation that enters the tube is
registered by the counter as a single count
• Number of counts in a given time is used to
measure count rate- number of counts divided by
time taken
• Before this count rate due to
background radiation
must be calculated
Geiger tube
Source in
Properties of radiation
• The count rate is then measured with the source
at a fixed distance from the tube without any
absorber present- background count rate is
taken away from this figure to give the TRUE
count rate from the source
• Count rate then measured with the absorber at a
fixed position between source and the tube
• True count rates with and without the absorber
present can then be compared
Properties of radiation
• The effect of the thickness of the absorber can be
compared by using absorbers of different
thickness of the same material
The graph shoes a set of measurements for the
absorption of β radiation by aluminium
(logarithmic scale)
Properties of radiation
The Geiger tube
• Sealed metal tube containing argon gas
• Thin mica window at the end allow α & β
radiation to enter
• Metal rod down the middle is at positive potential
• Tube wall connected to negative terminal of power
supply and is earthed
• When ionising radiation enters the tube it ionises
the gas atoms along its track
Properties of radiation
• Negative ions attracted to rod and positive ions to
the wall
• Ions accelerate and collide with other gas atoms
producing more ions
• More ions created in the same way so many are
created and discharged at electrodes in a short
• Pulse of charge passes round the circuit through a
resistor causing a voltage pulse across R (single
Properties of radiation
• Time taken for the tube to regain its nonconducting state after an ionising particle to
enter it is usually of the order 0.2ms
• Another particle entering the tube in this time
won’t cause a voltage pulse
• Count rate shouldn’t be greater than 1/0.2ms
Thin mica
High voltage
Tube wall
To pulse
About α, β and γ radiation
α radiation
• Composed of two protons and two neutrons
• Same as helium nucleus
• This was discovered by Rutherford
• 4x heavier than the nucleus of a hydrogen atom
About α, β and γ radiation
α radiation
• α particles collected as a gas in a glass tube fitted
with two electrodes
• When a voltage is applied to the electrodes the
gas conducted electricity and
emitted light
produced here
High voltage unit
• Using a spectrometer
can see that the tube is
Mercury to
Thin walled
filled with helium compress α
glass tube
About α, β and γ radiation
β radiation
• Consists of fast-moving electrons
• Proved by measuring the deflection of a beam of
particles using electric and magnetic fields
• Measured the specific charge, found to be the
same as electrons
• Created from a nucleus with too many neutrons
• Positron is emitted from an unstable nucleus
with too many protons
About α, β and γ radiation
γ radiation
• Photons with a wavelength with order 10-11m or
• Discovery made by using a crystal to diffract a
beam of γ radiation in a similar way to a beam of
light in a diffraction grating
About α, β and γ radiation
Inverse square law for γ radiation
Intensity, I, of the radiation is the energy
per second passing normally through unit
• For a point source emitting n γ photons per
second of energy hf, enerfy per second = nhf
• At a distance r from the source all the photos
pass through area 4πr2, constant = nhf/4πr2 so I
equals above equation
About α, β and γ radiation
• I varies with the inverse square of distance, r
• The experimental set up below shows how this is
Geiger tube
γ source
γ source
Sphere of radius, r
γ photons
entering tube
Photons emitted in
all directions
To scaler
Photons emitted in
all directions
About α, β and γ radiation
α radiation
β radiation
γ radiation
2 protons +
2 neutrons
β- = electron
β+ = positron
Photon of energy of
order MeV
Range in air
Fixed range
depending on energy
Up to about 1m
Follows inverse
square law
Deflection in
magnetic field
Easily deflected
Opposite direction to
α; less easily
Not deflected
Stopped by paper or
thin metal foil
Stopped by ~ 5mm of
Stopped by several
cms of lead
Produces about 104
ions per mm in air at
standard pressure
Produces about 100
ions per mm in air at
standard pressure
Very weak ionising
Energy of each
Constant for a given
Varies up to a
maximum for a given
Constant for a given
About α, β and γ radiation
• emission
• XY+α
β- emission
• X  Y + β- + e
β+ emission
• X  Y + β+ + νe
Electron capture
• X + e-  Y + ν e
A γ photon is emitted if
a nucleus has excess
energy after it has
emitted a α or βparticle
Dangers of radioactivity
Ionising radiation affects living cells because:
• It can destroy cell membranes which causes cells
to die
• Can damage vital molecules such as DNA
directly or indirectly by created ‘free radical’
ions. Damaged DNA can cause cells to divide
and grow uncontrollably
There’s no evidence of the existence of a threshold
level where cells will not be damaged
Dangers of radioactivity
• If using equipment that produces ionising radiation
a film badge must be worn
• Badge contains a strip of photographic film in a
light-proof wrapper
• Different areas of the film are covered by absorbers
of different thicknesses
• The amount of exposure to each form of radiation is
estimated by the blackening of the film
• If the badge is overexposed the worker cannot
continue working with the equipment
Dangers of radioactivity
• Dose of radiation is measured by the energy
absorbed by unit mass of matter from the
• Same dose of different types of radiation has
different effects
• Alpha particles produce more ions per mm than
gamma so it is more damaging
• Alpha radiation is more damaging inside the body
because it can’t penetrate the dead skin cells
outside the body
Dangers of radioactivity
Dose equivalent is the energy that would
need to be absorbed per unit mass of
matter from 250k of X-Radiation to have
the same effect as a certain dose of ionising
radiation, units: Sv (sievert)
Recommended limit of radiation exposure is
15mSv per year
Reality is much lower at the average radiation
exposure being exposed to 2mSv per year
Dangers of radiation
• All subjected to background radiation due to
cosmic radiation and radioactive material in
rocks, soil and in the air
10 8 3
37 0
Air (e.g. radon gas)
Ground and buildings
Food and drink
Cosmic ray s
Nuclear weapons
Air trav el
Nuclear power
Dangers of radiation
Storage of radioactive materials
• Should be in lead-lined containers. Most produce
gamma radiation as well as alpha and beta
• Lead lining of containers must be thick enough to
contain gamma radiation to about the
background level
• Regulations require the containers are kept under
‘lock and key’ and records are kept of contents
Dangers of radiation
Using radioactive materials
• No source should come into contact with the
• Solid sources  transferred using handling tools
such as tongs or a glove-box/robots. Ensures
that it is kept as far as practical from the skin
and beyond range of alpha/beta radiation
• Liquid/gas  should be in sealed containers
Radioactive decay
The half life, T1/2, of a radioactive isotope is
the time taken for the mass of the isotope to
decrease to half the initial mass
• Curve of the graph is a decay curve
• Mass of initial isotope decreases gradually as the
number of nuclei of the isotope decrease
• Mass of the isotope decreases
with time at a slower and
slower rate. Decrease
• exponentially
Radioactive decay
• After n half lives from the start:
• Decreases exponentially because radioactive
decay is random
• Number of nuclei that decay in a time is
proportional to the number of nuclei remaining
Radioactive decay
The activity, A, of a radioactive isotope is
the number of nuclei of the isotope that
disintegrate per second, units: Bq
• Activity is proportional to mass of the isotope
• Activity decreases with time
• For a radioactive source of activity A that emits
particles or photons of the same energy E, the
energy per second or Power of the source = AE
Theory of radioactive decay
• Every nucleus of a radioactive isotope has an
equal probability of undergoing radioactive decay
in a given time
• The number of nuclei that disintegrate in a certain
time interval depends only on the number of
nuclei present
• Number of nuclei that disintegrate is ΔN, it’s
proportional to:
- N, number of nuclei of X remaining at time, t
- the duration of the time interval Δt
Theory of radioactive decay
Decay constant, λ, is the probability of an
individual nucleus decaying per second units:
• Number of nuclei that decay, ΔN = -λNΔt
• Needs a minus sign because ΔN is a decrease
• Rate of disintegration = ΔN/Δt = -λN
• The rate of disintegration is also the activity, A, so
the above equation is the end result
• The solution of the equation is:
N = N0e-λt
Theory of radioactive decay
• Graph of number of nuclei against t represents the
equation N = N0e-λt
• The mass of a radioactive isotope can be found using the
equation: m = m0e-λt because
mass is proportional to number of
• The activity of a sample of N nuclei
of an isotope is in accordance to
equation: A = A0e-λt
• Corrected count rate is proportional
to the activity so: C = C0e-λt
Theory of radioactive decay
The graph of lnN against t is a straight line
The y-intercept = lnN0
The gradient = The N = N0e-λt equation can also be written in the
form lnN = lnN0 – t
• The longer the half life of a substance, the
smaller the decay constant because the
probability of decay per second is smaller
Radioactive isotopes in use
Carbon dating
• Living plants and trees contain a small amount
percentage of the radioactive isotope of carbon
because of cosmic rays knocking out neutrons
from nuclei
• Measuring the activity of carbon in dead wood
enables the age of it to be calculated, provided
the activity of the same mass of living wood is
Radioactive isotopes in use
Argon dating
• Rocks contain trapped argon gas because of the
decay of the radioactive isotope of potassium
• This happens when its nucleus captures an inner
shell electron
• A proton in the nucleus changed into a neutron and
a neutrino is emitted
(electron capture)
• Can also decay by 20
β- emission to form the calcium
isotope Ca. This is 8x more likely than electron
Radioactive isotopes in use
Radioactive tracers
• A radioactive tracer is used to follow the path of
a substance through a system. It should:
- have a half life stable enough for the necessary
measurements to be made, short enough to
decay quickly after use
- emit α or β radiation so it can be detected
outside the flow path
Radioactive isotopes in use
underground pipe
Tracer injected into flow- detector
on surface used to detect leakage
Contains β emitter or a γ emitter
as α radiation would be absorbed
by the pipes
Modelling oil
reservoirs to improve
oil recovery
Water containing tracer injected
into reservoir at high pressure,
monitor breakthrough of isotope
Tritiated water 3H2O, a β emitter
with a half-life of 12 years
Investigating uptake
of fertilisers by plants
Watered with solution containing
fertiliser. Measure radioactivity of
leaves to determine uptake
Fertiliser contains phosphorous
a β emitter with a half-life of 14
Monitoring uptake of
iodine by thyroid
Drink solution containing sodium
iodide. Activity of patient’s thyroid
compared to identical sample 24
hours later
Solution of sodium iodide
contains iodine a β emitter with a
half life of 8 days
Decay modes
• An N-Z graph shows the
neutron number against the
proton number for all known
• Stable nuclei lie along a bely
curving upwards with an
increasing neutron-proton
ratio from the origin
Decay modes
• For light isotopes (Z = 0-20)  stable nuclei
follow straight line N = Z
• As Z increases beyond 20  stable nuclei have
more neutrons than protons. The
neutron/proton ratio increases. Extra neutrons
help to bind the nucleons without introducing
repulsive electrostatic forces
Decay modes
• α emitters occur above the stability belt beyond
Z=60. Have more neutrons than protons but are
too large to stable. Strong nuclear force between
the nucleons is unable to overcome electrostatic
force of repulsion between protons
• β- occur to the left of the stability belt where
isotopes are neutron-rich
• β+ occur to the right of the stability belt where
isotopes are proton-rich. Electron capture also
happens in this region
Decay modes
• A nucleus that emits an alpha particle loses two
neutrons and two protons so moves diagonally
downwards to the left, across two grid squares
• A nucleus that emits a beta minus particle loses a
neutron and gains a proton so moves diagonally
downwards to the right across one grid square
• A nucleus that emits a beta plus particles loses a
proton and gains a neutron so moves diagonally
upwards to the right across one grid square
Decay modes
• An unstable nucleus may undergo a series of
isotopic changes involving alpha or beta
emission before it becomes stable
• Naturally occurring isotopes decay through a
series of such changes with one or more of the
changes having a long half life. This is why some
isotopes have not decayed completely
• Radioactive series are represented on the N-Z
graphs by a sequence of ‘decay arrows’
Decay modes
• After an unstable nucleus emits an α or β
particle/undergoes electron capture, it might
emit a γ photon
• Happens is the ‘daughter’ nucleus is formed in
an excited state
• This state is usually short lived and the nucleus
moves its ground state
• This can be represented by an energy level
Decay modes
Technetium generator
• Used in hospitals to produce a source that only emits γ
• Some form in an excited state after alpha or beta emission and
stay in this state long enough to be separated from the parent
• The long-lived excited state is a metastable state
• Nuclei of Tc isotope Tc 99-43 form in a metastable state after
beta minus emission from nuclei of molybdenum- half life of
• Tc 99-43(m) has a half life of 6h and returns to ground state
by γ emission
Decay modes
• Technetium generator consists of an ion
exchange column containing ammonium
Molybdenate exposed to neutron radiation
beforehand to make some of the Mo nuclei
• Solution of sodium chloride passed through the
column causes some chlorine ions to exchange
with Pertechnate ions not Mo ions, so solution
that emerges contains Tc 99-43(m)
Decay modes
Uses of Tc 99-43(m)
• Monitoring blood flow through the brain using
external detectors. Sodium pertechnate solution
is first administered intravenously
• Gamma camera images internal organs and
bones by detecting where γ photons have been
emitted by Tc 99-43(m)
Nuclear radius
• When a beam of high-energy electrons is directed
at a thin solid sample of an element
• The incident electrons are diffracted by the nuclei
of the atoms in the foil
• Beam is produced by accelerating electrons
through a pd of the order of a hundred million volts
• Electrons are diffracted by the nuclei because the
de Broglie wavelength of high energy electrons is
10-15m; about the same as the diameter of the
Nuclear radius
Electron beam
Thin metal sample
in a vacuum
Amplifier and
Detector reading
• A detector is used to measure the number of
electrons per second diffracted through different
Angle of diffraction
Nuclear radius
• Scattering of beam electrons is due to chargesame as alpha scattering but electrons are
attracted not repelled by the nuclei. Causes
intensity to decrease as angle increases
• Diffraction of beam electrons by each nucleus
causes intensity maxima and minima to be
superimposed on the effect above
• Happens provided the de Broglie wavelength of
the electrons in the beam is no longer than the
dimensions of the nucleus
Nuclear radius
• Superimposed intensity variations are similar to
concentric bright and dark fringes in a
monochromatic light diffraction grating
• Angle of the first minimum from the centre θmin,
is measured and used to calculate the diameter
of the nucleus- provided wavelength of the
incident electrons is known
Nuclear radius
• The radius, R, of different nuclides can be
measured by using samples of different elements
• Graph of lnR against lnA gives a straight line
with gradient 1/3 and y-intercept r0
• Graph of R against A1/3 gives a straight line
through the origin with gradient
• Graph of R3 against A gives a straight line
through the origin with gradient r0
Nuclear radius
• Nuclear volume, V, is proportional to the mass of
the nucleus- therefore density is constant and
independent of the radius
• Can conclude that nucleons are separated by the
same distance regardless of the size of the
nucleus and are therefore evenly separated
inside the nucleus
• In the volume formula above, m = Au where 1u =
1 atomic mass unit = 1.661 x 10-27kg
Nuclear Energy
Chapter 10
E = mc2
Energy and mass
• Calculate the increase in mass of a car of 1000kg
which gains 450kg
• E = mc2
• m=E
m = 450 x 103
m = 5 x 1012
3.0 x 108
Energy and mass
Energy changes in reactions
• Alpha decay
Momentum is conserved- momentum bef0re
equals momentum after
• Beta decay
Beta particles have variable KE, the neutrino
carries the rest of the energy
Energy and mass
Energy changes in reactions
• Electron capture
e- + X  Y + v + X-Ray. Neutrino carries charge
and conserves lepton number. X-Ray from outer
shells as inner shell ‘vacancy’ is filled
• Strong nuclear force
F = Q1Q2
E= Fxs
Binding energy
• Binding energy of the nucleus is the work
done to separate the nucleus into its
constituent neutrons and protons
• SNF pulls neutrons and protons together and
energy is released
• Mass decreases by Δm, the mass defect
• Δm = (Σ mass of n + p) – mass of nucleus
Binding energy
• Binding energy = Δmc2
Bi- atomic mass 212 and atomic number 83 has a
nucleus mass of 211.80012u. Calculate binding
energy of nucleus in MeV
• Δm = (83 x 1.00728) + (129 x 1.00867) –
211.80012 = 1.92255u
• Binding energy = 1.92255 x 931.3 = 1790MeV
Binding energy
Alpha particle tunnelling
• Two protons and two neutrons come together in
the nucleus
• They lose binding energy which becomes KE of
alpha particle
• KE < PE required to escape coulomb barrier
(electrostatic force)
• Alpha particle can act as a wave & so there is a
small probability that it can ‘tunnel’ through the
coulomb barrier
Binding energy
Nuclear stability
• An unstable nucleus requires more binding energy
than an a stable nucleus. Higher the binding energy
per nucleon, the more stable the nucleus because it
takes more energy to pull it apart
• Fusion  Small nuclei join together to make a
larger more stable nucleus, energy is released
• Fission  Large unstable nucleus splits into
smaller more stable fragments and energy is
Fission and fusion
Induced fission
• Looking to make new heavier elements/nuclei by
firing neutrons at U-235, but lighter elements
were found
• Uranium had split
• Energy released
• 2 or 3 neutrons were given off  chain reaction
Fission and fusion
Fusion reactors produce large amounts of power for
short periods of time
Energy is released by fusing deuterium and tritium to
produce nuclei of helium isotope and neutrons
Neutrons absorbed by lithium surrounding the reactor
vessel. Reaction produces tritium used in main reaction
Plasma is contained in steel container and heated by a
large current. Magnetic field stops plasma touching side.
Energy released per second more than is needed to heat
The thermal nuclear reactor
Pressurised Water Reactor
Fuel rods  U-238 (non-fissionable) enriched
with 2-3% U-235 (fissionable)
Control rods  Absorb neutrons to keep constant
Water  Moderator and coolant
Moderator  Slow fission neutrons down to allow
further fission- collide with moderator atoms
Critical mass  Fissionable materials must be
greater than a minimum mass for chain reaction
to occur
The thermal nuclear reactor
Comparing Pressurised Water Reactor to
Advanced Gas Reactor
Uranium oxide in
zirconium alloy cans
Uranium oxide in
stainless steel cans
Carbon dioxide gas
Coolant temp /K
Power output /MW
The thermal nuclear reactor
Safety features
• Thick steel vessel
• Containment building
• Emergency shut-down system
• Remote handling devises for sealed fuel rods
The thermal nuclear reactor
Radioactive waste
High Level
Fuel rods, U-235 and Pu- Sealed containers in
Intermediate Level
Radioactive material
with low activity
Stored in drums &
encased in concrete.
Stored in buildings with
reinforced concrete
Low Level
Lab equipment and
protective clothing
Sealed in metal drums &
buried in trenches
Thermal Physics
Chapter 11
Internal energy and temperature
Energy transfer between two objects takes place if:
• One object exerts a force on the other one
causing it to move
• Heat transfer is energy transfer due to a
temperature difference (conduction, convection
or radiation)
Internal energy and temperature
The internal energy of an object due to its
temperature is also called it’s thermal energy
Internal energy of an object changes as a result of:
• Heat transfer by radiation to or from the object
• Work done by the object, including electricity
If the internal energy of an object is constant, either:
• No heat/energy transfer due to radiation
• Heat/energy transfer and work done ‘balance each
other out
Internal energy and temperature
• Internal energy of a lamp filament increases
when the lamp is switched on because of work
done by the electricity supply pushing electrons
through the filament
• When it reaches its operating temperature, heat
transfer to the surroundings takes place and it
radiates light
• Work done by the electricity supply pushing
electrons through the filament is balanced by
heat transfer and light radiated from the filament
Internal energy and temperature
• In a solid  atoms and molecules are held to
each other by forces due to the electrical charges
of the nucleons. Molecules in a solid vibrate
randomly about fixed positions- the higher the
temperature the more the molecules vibrate. If
the temp is raised sufficiently the solid melts
because the molecules break free from each
The energy supplied to melt a solid raises the
potential energy of the molecules
Internal energy and temperature
• In a liquid  the molecules move at random in
contact with each other. Forces between the
molecules are not strong enough to hold them in
fixed positions. The energy supplied to a liquid to
raise its temperature, its kinetic energy increases
• In a gas  the molecules move about randomly
further apart than in a liquid
The internal energy of an object is the sum of
the random distribution of the kinetic and
potential energies of its molecules
Internal energy and temperature
Thermal equilibrium is when no overall
heat transfer occurs between two objects at
the same temperature
Temperature in ˚C = absolute temp in kelvins
– 273.15
The triple point of water, 273.16K is the
temperature at which ice, water and water vapour
are in thermal equilibrium
Internal energy and temperature
An object at absolute zero has minimum
internal energy pressure
No object can have a temperature below
absolute zero
ΔQ= mc(T2 – T1)
Specific heat capacity
The temperature rise of an object when it is heated
depends on:
• The mass of the object
• The amount of energy supplied to it
• The substance or substances which the object is
The specific heat capacity, c, of a substance is
the energy needed to raise the temperature of
unit mass of the substance by 1K without
change of state units: Jkg-1K-1
Specific heat capacity
The inversion tube experiment
• The gravitational potential energy of an object
falling in the tube is converted into internal energy
when it hits the bottom of a tube
• The tube is inverted each time the spheres hit the
bottom of the tube.
• The temperature of the lead shot is measured
initially and after a certain number of inversions
n= number of inversions; L= length of tube; T=
temp change
Specific heat capacity
Specific heat capacity of a metal
A thermometer is used to measure the
temperature change- water or oil acts as the
thermal contact
= (m1c1) x (mcalccal
Specific heat capacity
•Specific heat capacity of a liquid
• Electrical energy supplied = IVt
• Energy needed to heat liquid =
m1 x c1 x
• Energy needed to heat the
calorimeter = mcal x ccal x
Change of state
• Density of a gas is less than the density of the
same substance as a liquid or solid  molecules
are separated by large distances in a gas
• Atoms in a solid are locked together by strong
force bonds and so solids cannot flow like a
liquid or a gas. In a liquid or gas they are not
locked together because they have too much
kinetic energy
Change of state
Solid or liquid heated = more kinetic energy
Solid heated at its melting point: atoms
vibrate so much they break free from each other.
Energy needed to melt a solid at its melting point
is the latent heat of fusion
• Latent heat because no temperature change
happens even though the solid is being heated
• Fusion because the solid ‘fuses’ into a liquid as it
Change of state
Liquid heated at its boiling point: molecules gain
enough energy to overcome the bonds that hold them
together; form bubbles of vapour in the liquid. This is
the latent heat of vaporisation
• Latent heat released when a vapour condensesvapour molecules slow down as the vapour is
cooled- move slowly enough for the force bonds to
pull molecules together to form a liquid
• If solid vaporises directly when heated it’s known as
Change of state
Specific latent heat of fusion, lf: energy
needed to change the state of unit mass of
the substance from solid to liquid without
change of temperature, units: Jkg-1
Specific latent heat of vaporisation: energy
needed to change the state of unit mass of
the substance from liquid to vapour without
change of temperature, units: Jkg-1
Change of state
Graph showing what will happen if a pure solid is
heated to its melting point and beyond
Temp, T
l id
Time, t
Assuming no heat loss occurs during heating, and
energy is transferred at a constant rate P
If solid has a larger specific heat capacity than
liquid the liquid will heat up faster
Chapter 12
The experimental gas laws
Pressure of a gas is the force per unit area
that the gas exerts normally on a surface, it
depends on temperature, volume and
mass, units: Pa or Nm-2
The experimental gas laws
Boyle’s law
Measured how pressure of a fixed mass of gas
varies with volume. On a graph plotting 1/V gives
a straight line
T3 >T2 >T1
The experimental gas laws
Charles’ law
Measured the volume of a fixed mass of gas at
constant pressure varies with absolute
temperature- leads to the idea of absolute zero. No
matter how much gas is used, if the gas is an ideal
gas, it’s volume would be zero at absolute zero
273 373 Temp,K
The experimental gas laws
The pressure law
• Diagram shows how pressure of a fixed mass of
gas at constant volume can be measured at
different temperatures
• On a graph of pressure against
temperature in kelvins, it
gives a straight line through
the origin
The ideal gas law
• Molecules in a gas move at random with
different speeds
• When molecules collide they bounce off each
other/the surface without loss of speed
• Pressure of gas on a surface is due to the gas
molecules hitting the surface
• Each impact causes a tiny force on the surface
• Overall result is that the gas exerts a measurable
pressure on the surface
The ideal gas law
• The effect of individual molecules in a gas can be
seen if smoke particles are observed using a
• Their motion is called Brownian motion
• Motion of each particle is due to it being
bombarded unevenly at random by individual
• They’re subjected to a force due to the impacts
which changes its magnitude and direction
The ideal gas law
Brownian motion
Path of one
Smoke in
glass cell
Field of view
The ideal gas law
Avogadro constant
• The Avogadro constant, NA, is the number of
atoms in exactly 12g of  the value of NA is:
6.023 x 1023
• One atomic mass unit, u, 1/12th of the mass of a
1u = 1.661 x 1027kg
The ideal gas law
Molar mass
• A mole of a substance is the quantity of the substance
that contains NA particles
• Number of moles in a certain quantity of a substance
is its molarity
• The molar mass is the mass of 1 mole of the
1. Number of moles in mass MS of a substance =
MS/M where M is the molar mass of the substance
2. Number of molecules in MS = NAMS/M
The ideal gas law
• ideal gas is a gas that obeys Boyle’s law- the
three gas laws can be combined to make
One mole of any ideal gas, the value of pV/T is
equal to 8.31Jmol-1K-1
• This value is the molar gas constant, R
• For n moles of an ideal gas, the ideal gas
equation is above
The ideal gas law
the ideal gas equation
• MS of a substance is equal to its molar mass, M x
the number of moles, n
• The density of an ideal gas of molar mass = nM/V
= pM/RT
• Density of an ideal gas at constant pressure, is
inversely proportional to its temperature pV
• Substituting the number of moles, n, in
the equation pV=nRT with gives the
equation above
The kinetic theory of gases
Explaining Boyle’s law: the pressure of a gas is
increased by reducing its volume because the gas
molecules travel less distance between impacts
due to the reduced volume. More impacts per
second so pressure is greater
Explaining the pressure law: the pressure of a
gas is increased by raising its temperature.
Average speed if the molecules is increased by
raising the temperature- impacts are harder and
more frequent
The kinetic theory of gases
Molecular speeds
• Molecules in an ideal gas have a continuous spread
of speeds
• Speed of an individual molecule changes when it
collides with another gas molecule
• This is providing the distribution and temperature
stay the same
• Above equation shows the root mean square speed
of the molecules where N is the number of
The kinetic theory of gases
• If the temperature of a gas is raised the
molecules move faster on average
• Root mean square speed of the molecules
• Distribution curve becomes flatter and broader
No. of
Speed, v
The kinetic theory of gases
1. Molecules move with Random continuous
2. Molecules do not Attract each other
3. The collide Elastically
4. The Duration of the collisions are negligible
compared to the time between collisions
5. The Volume of one molecule is negligible
compared to the volume of the whole gas
The kinetic theory of gases
Proof of
1) Ft = 2mu1 ∴ F =
2) Time between collisions =
Combining equations =
3) Pressure, p = 
p for one molecule =
4) For N molecules p =
+ +…+
p= + +…+)
p= or or
5) Combining these equations by adding together means
3p = ( + + )
+ + =
∴ 3p =
6) pV = 1/3Nm