Download Radioactivity

Lesson 10
• Isotopes
• Radioactivity
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Discovery of Radioactivity
Theory of Radioactivity
Types of Radiations
Properties of Alpha (α ) Rays
Properties of gamma (γ) rays
Properties of beta (β) particles
Geiger-Müller tube
Cloud Chamber
Radioactive Decay
Half-Life
• Energy Levels
Isotopes
A Review of Atomic Terms
• Nucleons – particles found in the
nucleus of an atom
– neutrons
– protons
• Atomic Number (Z) – number of
protons in the nucleus
• Mass Number (A) – sum of the
number of protons and neutrons
• Isotopes – atoms with identical
atomic numbers but different
mass numbers
• Nuclide – each unique atom
Isotopes
• Main Sub-atomic Particles
a For stable nuclides, the isotopic abundance is given; this is the fraction of atoms of this type found in a typical sample
of the element. For radioactive nuclides, the half-life is given.
b Following standard practice, the reported mass is that of the neutral atom, not that of the bare nucleus.
c Spin angular momentum in units of ћ.
Isotopes
What’s an isotope?
Two or more varieties of an element
having the same number of protons but
different number of neutrons. Certain
isotopes are “unstable” and decay to
lighter isotopes or elements.
Deuterium and tritium are isotopes of hydrogen. In
addition to the 1 proton, they have 1 and 2
additional neutrons in the nucleus respectively*.
Another prime example is Uranium 238, or just
238U.
Radioactivity
• Radioactivity – the spontaneous decomposition
of a nucleus forming a different nucleus and
producing one or more additional particles
• Nuclear Equation – shows the radioactive
decomposition of an element
14 C
6
→ 147N +
0 e
-1
• Nuclear Forces – strong nuclear force holds
neutrons and protons together to form a nucleus
(counters electromagnetic repulsion). Weak
nuclear force operates within individual nucleons
and gives rise to some kinds of radioactivity
Discovery of Radioactivity
• Antoine Henri Becquerel (1852-1908)
 Henri Becquerel in 1896 discovered that uranium
compounds emitted invisible radiation, which could:
 blacken a photographic plate
 ionize a gas
 Noticed the fogging of photographic plate by uranium
crystals
• Pierre Curie (1859-1906), Marie Curie (1867-1934)
 Further studies of uranium and discovery of polonium and
radium. Marie received two Nobel prizes. She died from
the effects of radiation doses received during her
experiments
• Ernest Rutherford (1871-1937)
 His understanding of atomic structure helped us
understand the role of the nucleus.
Theory of Radioactivity
• Some Terminology
• A neutral atom has equal numbers of protons in its nucleus and
electrons in orbit about the nucleus.
• An atom can gain or lose electrons, becoming a negative or positive ion
• The proton number (or atomic number) Z of an element is the number
of protons in each nucleus of the atoms of the element. All its nuclei
have the same proton number
• The nucleon number (or mass number) A of an atom is the number of
nucleons (protons plus neutrons) in its nucleus
• A given element can have several values of A, since the number of
neutrons can vary. Atoms of an element with equal numbers of
neutrons constitute an isotope of that element
• A nuclide refers to the nucleus of an atom, characterized by its A and Z
value, or to an atom to which such a nucleus belongs
Theory of Radioactivity
Hydrogen has 3 isotopes:
Note: Chemical reactions only involve the outer electrons of atoms, so isotopes of a given element act the same chemically. For
example, the most common form of water is made up of molecules of H2O. But there also exist water molecules, about 1 part in
5000, in the form of D2O (‘heavy water’).
Theory of Radioactivity
•
Ionization occurs when neutral atoms have electrons knocked off them, producing
positive ions and free electrons.
• Radioactivity is simply the spontaneous disintegration of nuclei to move from
an unstable state to a stable one.
• There are three types of radiation emitted in radioactive decay: alpha particles,
beta particles and gamma rays.
• Alpha Particles(α)
• These are helium nuclei, and therefore consist of two protons and two
neutrons.
• Beta Particles (β- β+)
• There are two types of beta particle: beta-plus and beta-minus. The beta-plus
is sometimes called an anti-electron. Each can travel up to 98% the speed of
light. A beta-minus particle is released as a result of a neutron changing into a
proton, while a beta-plus particle is released as a result of a proton changing
into a neutron.
• Gamma Rays (γ)
• Gamma rays are high energy, short wavelength photons of electromagnetic
radiation. Gamma rays are emitted because the atom is usually in a high
energy state after emission of alpha or beta particles. This unstable state is
made stable by emission of gamma ray photons.
Theory of Radioactivity
• A strip of polythene or a strip of Perspex rubbed with wool
become charged by friction, negatively and positively
respectively. If one of them is held close to the cap of the
electroscope, and the cap is momentarily touched with a
finger, the cap acquires a charge opposite to that of the
charged strip.
• When the strip is removed, the charge spreads itself around
the cap, the rod and the gold leaf.
• The leaf is seen to diverge, since it and the metal rod have the
same charge.
Theory of Radioactivity
• When a radium source (held in tongs, and well away from
the face) is held close to the cap, without touching it, the
leaf is seen to collapse. This is due to the ionization of the
air produced by the radiation emitted by the radium, which
produces positive ions and negative electrons. If the cap is
negative it attracts the ions, and if it is positive it attracts
the electrons. In either case the electroscope is neutralized.
The Electroscope
Types of Radiation
• They can be separated by a magnetic field, since those
that are charged will be deviated:
• A dark spot is produced on the photographic plate,
where impacted by radiation.
Types of Radiation
• From the directions of the deflections produced by the magnetic field
(using Fleming's left hand rule - covered in other notes) we can infer
that:
• The gamma rays are uncharged, since they are undeviated. They are
now known to be electromagnetic radiation of the shortest known
wavelength
• The alpha particles are positively charged. They are now known to be
helium nuclei
• The beta particles are negatively charged. They are now known to be
electrons
• Note: The above diagram is something of a ‘composite’ - it indicates the
relative directions of the deflections but not the true relative sizes of
deflections. Since alpha particles are helium nuclei, they are 1000s of
times more massive than beta particles (electrons) - if the magnetic field
were strong enough to move the alphas by the amount indicated, the
betas would be deviated so much as to not reach the plate.
Properties of Alpha (α ) Rays
• An alpha particle is an helium nucleus ( 42 He)
• The alpha particles short out of radioactive substances have
velocities ranging from (1.4-1.7)x107m/s
• They produce high ionisation in the gas through which they
pass. (α ) particles have 100 times than beta (β) and about
10,000times that of gamma (γ) rays.
• They feebly affect photographic paper
• They are scattered by nuclei of heavy elements such as gold
and produce heat due to the stoppage of (α ), (β) and (γ) by
the radioactive substance.
• Radium-226 (‘Ra-226’) is an alpha source.
Properties of gamma (γ) rays
• They are E-M waves of short wavelengths (0.005Å to 0.5Å).
They are not charged, hence not affected by either electric
or magnetic field and travel with the speed of light.
• They produce fluorescence and affect photographic plate.
• They ionise the gas through which they pass but the
ionisation is small
• They are more penetrating than even beta particles and
can pass though an iron plate of about 30 cm thickness.
Several cm of lead or several metres of concrete are
required to absorb them significantly. Cobalt-60 (‘Co-60’) is
a gamma source.
• They are diffracted by crystals just like X rays are.
Properties of beta (β) particles
• The beta particles possess –ve charge and mass equal to that of an
electron. They are identical to electrons
• All (β) emitted from a substance do not have the same velocity.
They range from 0.3c to 0.99c. At high velocities, e/m is found to
decrease , indicating an increase in mass according to the equation
m
m0
1
v2
c2
• The ionising power is low hence the range is large
• They affect photographic plate and produce fluorescence in certain
compounds e.g. barium platino cyanide
• They are deflected by electric and magnetic fields, their direction
indicating that they are negatively charged particles.
• They penetrate through thin foils and their penetration power is
greater than that of alpha rays.
• Strontium-90 (‘Sr-90’) is a beta source.
Geiger-Müller tube (‘GM tube’)
• The Figure shows the experimental arrangement of Geiger and
Marsden.
• Their alpha source was a thin-walled glass tube of radon gas. The
experiment involves counting the number of alpha particles that are
deflected through various scattering angles φ.
The dots are alphaparticle scattering data for
a gold foil, obtained by
Geiger and Marsden. The
solid
curve
is
the
theoretical
prediction,
based on the assumption
that the atom has a small,
massive,
positively
charged nucleus. The data
have been adjusted to fit
the theoretical curve at
the experimental point
that is enclosed in a circle.
Geiger-Müller tube (‘GM tube’)
A Geiger-Müller tube (‘GM tube’) - a pulse of current is
produced when it detects radiation. It can be connected to a
scaler or a ratemeter. A scaler counts the number of pulses. A
ratemeter gives the average number of pulses per second or
per minute, and may give a click for each pulse (a ‘Geiger
counter’).
Cloud Chamber or Bubble Chamber
• Though we cannot see radiation directly, we can see where it has
been using these devices. A cloud chamber contains vapour and as
an alpha particle, for example, passes though, it collides with
atoms, producing a path of ions. Vapour condenses along the path
of ions, making it visible. A bubble chamber contains liquid, and
vapour bubbles are formed along the ion path, again making it
visible.
• Alpha particles are strongly ionizing and lose their energy quickly,
and being relatively massive, they are not easily deflected by
impacts - so they produce short, thick, straight paths
• Beta particles are less strongly ionizing, and being light are easily
deflected - so they produce long, thin, irregular paths
• Gamma rays can eject electrons from atoms, and these produce the
paths seen
Radioactive Decay
Types of Radioactive Decay
• Alpha-Particle Production
Alpha particle – helium nucleus
– Examples
• Net effect is loss of 4 in mass number and loss of 2 in atomic
number.
Radioactive Decay
• Beta-Particle Production
Beta particle – electron
– Examples
• Net effect is to change a neutron to a proton.
Radioactive Decay
• Gamma Ray Release
•
Gamma ray – high energy photon
– Examples
• Net effect is no change in mass number or atomic
number.
Radioactive Decay
• Positron production
•
Positron – particle with same mass as an electron but with a positive charge
(antimatter version of an electron)
– Examples
• Net effect is to change a proton to a neutron.
Radioactive Decay
• Electron capture
• Inner orbital electron is captured. New nucleus formed.
Neutrino and gamma ray produced
20180Hg + 0-1e → 20179Au + ν + 00γ
• Net effect is to change a proton to a neutron
Law of radioactive disintegration
Let N be the number of atoms present in a particular radioactive element at a given time t.
dN
is proportional to N (the number of un decayed
dt
then the rate of decrease (decay)
dN
dt
particles) or
dN
dt
N
N
N , or A=
Where λ is a constant known as the disintegration constant of the respective element. It is
defined as the ration of the amount of the substance which disintegrates in unit time to the
amount of substance present
dN
dt
N
dN
N
N0
N,
dN
N
dt
t
dt,
ln
N
N0
t
t
0
,
ln
0
N
N0
e
N
N0e
t
N
N0
t
,
t
(1)
This equation shows that the number of atoms of a given radioactive substance decreases
exponentially with time.
Half-Life
• The “half-life” (h) is the time it takes for half the atoms of a radioactive substance to
decay.
• For example, suppose we had 20,000 atoms of a radioactive substance. If the half-life is 1
hour, how many atoms of that substance would be left after:
Time
#atoms
remaining
% of atoms
remaining
1 hour (one lifetime) ?
10,000
(50%)
2 hours (two lifetimes) ?
5,000
(25%)
3 hours (three lifetimes) ?
2,500
(12.5%)
Half-Life
As nuclei in a radioactive sample decay, the activity gets less, till eventually there are no more
nuclei left to decay.
The half-life of a radioactive source is the time for the activity to fall by half
Or, since the activity of a source is directly proportional to the number of undecayed nuclei, then:
The half-life of a radioactive source is the time for half the undecayed nuclei to decay
Half-Life
From equation (1) above if T 1 is the half life period, the time required for half of the
2
radioactive substance to disintegrate from N 0
N0
2
N0e
T1
2
T1
2
,
T1
2
e
ln e
to
NO
then
2
1
,
2
1ln 2,
T1
2
T1
2
ln 2
ln 2
0.693
(2)
Substitute equation (2) in (1), then we have
N
N0
so
ln 2 t
T1
e
2
the
N
N0
ln 2 (
e
t
1
T
2
,
fraction
but
e
ln 2
remaining
0.5
after
some time
t
is
given by
t
T1
(0.5)
2
λ (lambda) is a positive constant called the decay constant. It has the unit s-1 , hr-1, day-1
or yr-1
The minus sign is included in A=
increases.
N because N decreases as the time t in seconds (s)
Half-Life
The decay constant λ of a radioactive nuclide is the probability that an individual nucleus will
decay within a unit time.
The value of λ is constant for any particular nuclide and zero for a stable nuclide.
Nuclear Fission
Nuclear fission
Means splitting up
A large nucleus (A 200 ) splits into two. The daughter fragments have higher binding energy
than the parent. They are more stable.
It was found (in 1939) that if uranium was bombarded with neutrons (these have no charge and
are not repelled by the nuclei), that a uranium nucleus could be split into two nuclei. This is
nuclear fission (it is not the same as spontaneous radioactivity).
One such splitting is:
e. g
235
92
U
1
0
n
236
92
141
56
Ba
92
36
Kr 301 n Energy
Nuclear Fusion
Nuclear fusion
Means joining together. Nuclear fusion: two (or more) atomic nuclei form a single heavier
nucleus. The reaction only takes place at very high densities and temperatures.
There are many examples of fusion reactions. The fusion of deuterium with tritium to make
helium (plus a neutron) is one of the more common ones -. Termed the D-T reaction.
2
1
H
3
1
H
4
2
He
1
0
2
1
1
1
n
Other examples incude:
1
1
H
3
2
He
1
1
H
3
2
He
2
1
H
4
2
0
1
0
0
He 211H
energy,
H
H
3
2
H
0
0
energy, and
energy
The fusion reaction of two (or more) nuclei with masses lower than iron is exothermic (heat
given out).
Conversely, the fusion reaction of two (or more) nuclei with masses greater than iron is
endothermic (heat absorbed).
Applications of Radioactivity
i. Many satellites use radioactive decay from
isotopes with long half-lives for power because
energy can be produced for a long time
without refueling.
ii. Isotopes with a short half-life give off lots of
energy in a short time and are useful in
medical imaging, but can be extremely
dangerous.
iii. The isotope carbon-14 is used by archeologists
to determine age.
Applications of Radioactivity
iv.
Sterilizing
• Gamma rays can kill bacteria, which makes them useful for sterilizing
medical instruments after they have been sealed. A disposable syringe, for
example, would be sealed in a plastic container and the container then
exposed to gamma rays, killing the bacteria inside.
v.
Controlling thickness
• The amount of beta particles absorbed by the paper depends on its
thickness. The gap between the rollers can be automatically adjusted,
keeping the beta count rate, and therefore the thickness of the paper,
constant.
• Alpha particles are not used since they are completely absorbed by even
thin paper. Gamma rays are not used because they would not be absorbed
at all by the paper.
• A similar process to the above can be used to automatically control the
thickness of steel sheet, but in this case a gamma source would be used.
Applications of Radioactivity
vi.
Nuclear-Energy Power Plants
Harmful Radiation
• Radiation becomes harmful
when it has enough energy
to remove electrons from
atoms.
• The process of removing an
electron from an atom is
called ionization.
• Visible light is an example of
nonionizing radiation.
• UV light is an example of
ionizing radiation.
Harmful Radiation
• Ionizing radiation absorbed by people is measured
in a unit called the rem.
• The total amount of radiation received by a person
is called a dose, just like a dose of medicine.
• It is wise to limit your exposure to ionizing radiation
whenever possible.
• Use shielding materials, such as lead, and do your
work efficiently and quickly.
• Distance also reduces exposure.
Sources of Radiation
• Ionizing radiation is a natural part of our
environment.
• There are two chief sources of radiation you will
probably be exposed to:
– background radiation.
– radiation from medical procedures such as x-rays.
• Background radiation results in an average dose
of 0.3 rem per year for someone living in the
United States.
Background Radiation
• Background radiation levels
can vary widely from place
to place.
– Cosmic rays are high energy
particles that come from
outside our solar system.
– Radioactive material from
nuclear weapons is called
fallout.
– Radioactive radon gas is
present in basements and the
atmosphere.
Energy Levels
• In an atom, electrons around a central nucleus
can only have particular energy values. These
discrete values are termed 'energy levels'.
In a diagram they are represented by
horizontal lines, with the lowest level (the
ground state) at the bottom and the highest
level (ionisation) at the top.
Energy Levels
The following is an energy level diagram for hydrogen:
The ionisation energy of an atom is the minimum energy needed to completely remove an
electron from the atom in its ground state. For hydrogen, the ionisation energy = 13.6eV =
21.8x10-19J
Energy Levels
BOHR’S POSTULATES
1. Electrons occupy “stationary states”(they do not radiate)
2. These orbits are quantized
We can account for spectral lines if , angular momentum is L
mvr
Pr
nh
2
n ,
n = 1,2,3,4,…….
Also P
h
,
so,
pr
hr
nh
,
2
n
2 r or
The circumference is a number of de-Broglie wavelengths
3. Transition between states leads to absorption/emission of a photon with energy
hf
E1
E2
Nuclear Models
Each model has its own merit. Realize the concept of these models and apply
them to explain nuclear phenomena such as nuclear decay and nuclear reactions.
Liquid drop model: strong force hold nucleons together as liquid drop
of nucleons (Bohr). Rnucleus = 1.2 A1/3.
Gas model: nucleons move about as gas molecules but strong mutual
attractions holds them together (Fermi).
Shell model: nucleons behave as waves occupying certain energy states
worked out by quantum mechanical methods.
Each shell holds some magic number of nucleons.
Magic numbers: 2, 8, 20, 28, 50, 82, 126. Nuclei with magic number of protons or
neutrons are very stable.
The shell model
Quantum mechanics treats nucleons in a nucleus as waves.
Each particle is represented by a wavefunction.
The wavefunctions are obtained by solving a differential equation.
Each wavefunction has a unique set of quantum numbers.
The energy of the state (function) depends on the quantum
numbers.
Quantum numbers are:
n = any integer, the principle q.n.
l = 0, 1, 2, ..., n-1, the orbital quantum number
s = 1/2 or -1/2 the spin q.n.
J = vector sum of l and s
The wavefunction
n,l
is even or odd parity.
The Shell Model
Energy Level Diagram of Nucleons
n
l
j
7
6
6
6
6
6
6
0
1
2
3
4
13
6
5
5
5
5
5
0
2
3
4
11
5
4
4
4
4
Notation
Shell
total
1i
3p
3p
2f
2f
1h
14
2
4
6
8
10
~126
/2 –
½+
3
/2 +
5
/2 +
7
/2 +
1h
3s
2d
2d
1g
12
2
4
6
8
~82
4
0
1
2
9
/2 +
½–
3
/2 –
5
/2 –
1g
2p
2p
1f
10
2
4
6
~50
3
7
1f
8
~28
3
3
3
0
1
2
2
0
1
1
0
/2 +
½–
3
/2 –
5
/2 –
7
/2 –
9
/2 –
(2j+1)
/2 –
J+
Some Excited States of the 7Li
Nuclide
½ + ___________ 6.54 MeV
½+
/2 +
5
/2 +
2s
1d
1d
2
4
6
~20
3
½–
/2 –
1p
1p
2
4
~8
½+
1s
2
~2
3
Energy states of nuclei are
labelled using
J = j1 + j2 + j3 + j4 + ...
plus parity,
7/
2
+ ___________ 4.64
½ – ___________ 0.478
3/ – ___________ Ground State
2