26 pius augustine nucleus and radioactivity

Dr. Pius Augustine, SH College, Kochi

Can e-m radiation be used for seeing
nucleus? Comment
Hint:
Can feel the presence of a bottle on a table
in a dark room by making a large sound in
the room?

Sir James Chadwick
(1891 –1974)

Quark model of neutron

Neutron
Neutral subatomic particle discovered by Chadwick
Constituent of every atomic nucleus except ordinary
hydrogen.
It has no electric charge and a rest mass equal to
1.67493 × 10−27 kg
Mass - marginally greater than that of the proton but
nearly 1,839 times greater than that of the electron.

Neutron
Discovered by James Chadwick, English
physicist in 1932, was awarded Nobel prize.
Produced by bombarding beryllium with α
2He4 + 4Be9
6C12 + 0n1 + Q.
Zero charge and mass greater than
proton

Neutron
Collapsed H- atom
At extreme temperature and pressure the
electron of the H atom was forced
towards proton.
Before the electrons bangs into the proton,
it was stopped close to proton by nuclear
energy Dr. Pius Augustine, SH College, Kochi

Neutron Properties
i. Fundamental particle in the atom except H-
atom
ii. No charge and not deflected in E and B
iii. High penetrating power and low ionizing
power
iv. In free state, it is unstable and decays
n p + β + υ
v. Spin ½ particles (Fermions–obey FD statistics)

Classification of Neutrons
Based on Kinetic energy (velocity)
i. Slow neutrons: 0 to 1000 eV . They are
in thermal equilibrium with the medium
through which they pass and are called
thermal neutrons.
Slow neutrons are used in nuclear reactors.
When interact with 10B, will form 7Li and 4He.
Hence B-is used as slow neutron absorber in reactors to
control the fission. Dr. Pius Augustine, SH College, Kochi

Classification of Neutrons
Based on Kinetic energy (velocity)
ii. Fast neutrons : 0.5 to 10 MeV.
When pass through material, slowed down by
collisions with the nuclei of the material and
lose a part of their energy.
Moderators: Materials rich in hydrogen are very
efficient in slowing down neutrons. (heavy
water, graphite)

Isotopes
Atoms of the same element whose nuclei
have same atomic number Z, but differ in
their mass number A
Around 400 stable siotopes
Eg. 1H1, 1H2 , 1H2
6C12 , 6C13, 6C14

Isobars
Atoms of different elements having the
same mass number A, but different
number of protons (atomic number Z)
Eg: 18Ar40 and 20Ca40
12Mg24 and 11Na24

Isotones
Atoms of different element, but nuclei
having equal no. of neutrons.
Eg. 6C14 , 7N15, 8O16
14-6 = 15-7 = 16-8 = 8 neutrons

Isomeric nuclei or isomers
Nuclei having same Z and A, but different
from one another in their nuclear energy
states and exhibits differences in their
internal structure.
Differ in the manner of radioactive decay
They are distinguished by their different life
times. Dr. Pius Augustine, SH College, Kochi

Isodiaphers
Nuclides which have different atomic numbers
and mass numbers but the same neutron
excess
Neutron excess - difference between numbers of
neutrons and protons in the nucleus.
90TH234 and 92U238
Thorium – P=90 n = 144 n-p = 54
Uranium - P=92 n = 146 n-p = 54

Is it a general behavior associated with alpha decay?
Analyze a few more alpha emissions.

Mirror Nuclei
Same A, but with proton and
neutron number interchanged
Eg. 4Be7 and 3Li7

Nuclear size
Alpha particle scattering experiments -Smallest
value of distance of closest approach was
found to be 10-14 m to 10-15m which is nuclear
radius
Nuclear radius R = roA1/3
ro = 1.3 fm
Size of atom (10-10m) is 10,000 time nucleus

By what factor must the mass number
of a nucleus increase to double its
volume?
To double it radius?

Atomic mass unit (a.m.u) or 1 u
1a.m.u is equal to 1/12th mass of one 6C12 atom.
Atomic mass of 12C is 12u.
12 x10-3kg C contains 6.023 x1023atoms
1amu or 1u = 1.660 x 10-27kg
1u = (1/12) (12g/mol)(1mol/6.022x 1023)
= 1.66 x 10-24 g
Using E = mc2 1u = 931MeVDr. Pius Augustine, SH College, Kochi

Particle Mass (kg) Mass (u) Mass (MeV/c2)
1 amu 1.660540 x 10-27 kg 1.000 u 931.5 (MeV/c2)
Neutron 1.674929 x 10-27 kg 1.008664 u 939.57 (MeV/c2)
Proton 1.672623 x 10-27 kg 1.007276 u 938.28 (MeV/c2)
Electron 9.109390 x 10-27 kg 0.00054858 u 0.511 (MeV/c2)

Mass of proton = 1.007276 amu
Mass of neutron = 1.008665 amu
mn > mp

Nuclear mass
Expected mass of nucleus - sum of the
mass of protons and neutrons present
M = Zmp+ (A-Z)mn
Experimental value of nuclear mass is less
than this expected value
Note: Atomic Mass is the mass of complete atom
(Nucleus + electrons)
Nuclear mass – mass of nucleus

Mass defect Δm
Real nuclear mass < Zmp+ (A-Z)mn
Difference between real mass of
nucleus and expected mass is called
mass defect

Nuclear density (ρN )
Nuclear mass = A mn A – mass no.
Mass of nucleon (mn) = 1.67 x 10-27kg
Nuclear volume = (4/3) πR3
= (4/3) π {roA1/3}3
ρN = MN / (4/3) πro
3
= A mn /(4/3) π ro
3A
= 1.816 x 1017kg/m3.(≈ white dwarfs)

The most common kind of iron nucleus has a
mass number of 56. Find the radius, aproximate
mass, and aproximate density of the nucleus.
R = roA1/3 = 4.6 fm ro = 1.2 fm.
Mass = 56 x 1.66 x 10-27 = 9.3 x 10-26 kg.
Density = M/V = 2.3 x 1017 kg/m3.

Nuclear spins
Electons, protons and neutrons are spin ½ particles.
Spin angular momentum of nucleon S = [½ (½ +1)]1/2 h/2π
Z- component of angular momentum Sz = ±½ h/2π
Nucleons have orbital motion in addition to spin motion
and hence there is total angular momentum (J) called
nuclear spin

Nuclear spins and magnetic moments
Like electrons magnetic moments (Bohr magneton μB =
eh/4πme), nucleons also have magnetic moment due to
this angular momentum
(Nuclear magneton μN = eh/4πmP= 5.05079 x 10-27 J/T
mp – proton mass (1836 times me)
μN = μB/1836
Z component of magnetic moments of proton = 2.7928 μN
Z component of magnetic moments of neutron = -1.9130 μN

Binding energy
Energy equivalent to mass defect.
When nucleus is formed mass defect is converted
into energy (= Δmc2) (Released)
To disrupt a stable nucleus into its constituent protons
and neutrons, minimum energy required = B.E.
ie. if B.E is more, nucleus is more stable

B.E /nucleon (BEN) and Packing fraction
B.E / nucleon
= B.E / mass number
Packing fraction = mass defect per
nucleon
Packing fraction = Δm / A

Calculate the mass defect and binding energy of deuteron. The
mass of deuteron mD = 3.34359 x 10-27 kg or 1875.61 MeV/c2
Z = 1 A = 2
∆m = mp + mn - mD
mn = 939.57 (MeV/c2)
mp = 938.28 (MeV/c2)
mD = 1875.61 MeV/c2
∆m = 2.24 MeV/c2.
B.E = ∆m x c2
= 2.24 MeV
Note: More than two million (2.24
MeV) electron volts are required to
separate simplest deuteron into
proton and neutron.
This very large value shows the
strength of nuclear force.

Calculate the binding energy per nucleon of an
alpha particle from the given data.
Z = n = 2 A = 4
B.E = [2mp + 2mn] – m(4He) c2
mp = 1.007825 u
mn = 1.008665 u
m(4He) = 4.002602 u
1 u = 931.5 MeV/c2
B.E = 28.3 MeV
BEN = BE/4 = 7.07 MeV/nucleon
For H-isotopes BEN is 2
to 3 Mev/nucleon.
So He nuclei cannot be
broken down to
hydrogen isotopes
without giving energy

40 80
Max
stabilityFusion Fission

Because it has the highest binding energy per nucleon of all
nuclides, 28Ni62 may be described as the most strongly bound. Its
neutral atomic mass is 61.928349 u. Find its mass defect, its total
binding energy, and its binding energy per nucleon.
Z = 28 mH = 1.007825 u n = 34, mn = 1.008665 u and M = 61.928349 u
∆m = mp + mn - M = 0.585361 u
= 0.585361 x 931 = 545.3 MeV.
This much energy is required to separate 62 nucleons
B.E/nucleon = 1/62 = 8.795 MeV/nucleon
∆m = 0.585361 u is about 1% of the mass of the nucleus
ie. B.E/nucleon will be about 1% of the rest mass energy of a
nucleon. Which means it will be very stableDr. Pius Augustine, SH College, Kochi

Calculate the mass of an alpha particle. Given B.E = 28.2 MeV
Alpha particle contains 2p and 2n
mH = 1.007825 u mn = 1.008665 u
MHe. = 2 x1.007825x 931 MeV + 2 x 1.008665 x 931 Mev –28.2
MeV
= 28.2 MeV

If the nucleons of a nucleus are separated from
each other, the total mass is increased. Where
does this mass come from?

Discussion of graph
i. B.E/A increases with A and after
attaining a flat max, it decreases.
ii. Max for intermediate (A) nuclei,
(nucleons are most tightly bound)

Discussion of graph
iii.At multiple of 4 (4,8,12,16 …) shows
sudden rise.
iv. B.E/A is 8 MeV for nearly all elements
except very light (fusion)and heavier
(fission) elements.

Reason for variation in B.E
B.E is due to interaction of nucleons.
Surface nucleons B.E is less.
Surface to Volume ratio is greater for light nuclei
[4πR2/(4/3)πR3]
As R decrease, reduction in volume is more prominent
than surface effect due to (R3) dependence
ie. proportionately large surface area in light
nuclei - surface nucleons more in number

Play by substituting various numbers (size of the nucleus!)

Reason for variation in B.E
Electrostatic repulsion (p-p) introduce –ve
BE (proportional to q1q2)which increases as
the square of no. of protons, which is the
reason for reduction in B.E of heavy
nuclides
A balance of the surface effect and
electrostatic effect are seen in the middle
range nuclei. Dr. Pius Augustine, SH College, Kochi

Significance of average B.E /nucleon = 8 MeV
It explains saturation nature of nuclear force.
One nucleon does not interact with all other
nucleon but only with certain no which gives
saturation
Note: if a nucleon was interacting with all other
nucleons, B.E/nucleon would have increased
linearly with A.

Nuclear Force - a few points
Force that binds p and n inside nucleus, despite the
electrostatic repulsion of protons.
It does not depend on charge (P-P, P-n and n-n forces)
Short range of the order of nuclear dimensions 10-15 m.
(Otherwise nucleus would grow pulling more nucleons in to
it)
Within the acceptable range, it is much stronger that
electrostatic force.

Nuclear Force – a few points
Nearly constant nuclear density and constant
nuclear B.E/nucleon of large nuclides
established that nuclear force exhibit
saturation property.
ie.a particular nucleon cannot interact with all
other nucleons in the nucleus, but only with
those in the immediate viscinity.
(Electrical force is different from this – infinite range)

Nuclear Force – pairing up
Nuclear force favors binding of pairs of p or n
each having opposite spins. (Pauli’s principle)
It shows pairs of pairs – interaction between pair
of protons with pair of neutrons.
Alpha particle is exceptionally stable in its mass
number.

Nuclear Force – tensor force
Nuclear force is a spin dependant force
It is a non central force (tensor force)
Consider two pairs of neutrons. In each pair, the
separation between the neutrons is the same. Can the
force between the neutrons have different magnitudes
for the two pairs?

Nuclear Models
Liquid Drop Model- Semiempirical mass formula
Shell Model and Magic numbers
Collective Model – collective rotation and vibration
Will be discussed in the next PPT file.

Radioactivity

Radioactivity? Two radioactive substances?
Phenomenon of spontaneous emission of
powerful radiations from the nucleus of
heavy elements.
Radioactive elements: uranium, Thorium, Radium
and Polonium
Compare with definition of poetry – spontaneous overflow of
powerful emotions recollected in tranquility.
But radioactivity is dangerous!!!

Light atoms (eg. He) p = n
Massive elements (U235 p
= 92 n = 143) n >>p
Particles below the line
(see B) will decay by beta
plus (positron) emission
Particles above (see A) will
decay by beta minus
emission.
Neutron number (n) vs Proton number (Z)

SegreChart
238Udecayseriesto206Pb
Timesarehalflives

A radioactive substance is oxidized. What
changes would you expect to take place in the
nature of radioactivity?
No change
Radioactivity is a nuclear
phenomenon
Oxidation is electronic.Dr. Pius Augustine, SH College, Kochi

A small hole is drilled in a lead block and a
piece of radioactive element is placed in it.
Radiations emitted from the radioactive
element can escape only through the hole
and others are absorbed by the lead wall.
Radioactivity Experiment

Radioactive radiations in electric field
α – towards –ve plate
β - towards +ve plate
γ - undeflected

Radioactive radiations in magnetic field
Alpha and Beta particles
are oppositely charged.
Beta particles bent more
(semicircle) – lighter
compared to alpha.
Gamma is uncharged -
undeflected
Uniform B is applied
perpendicular to plane of the
screen.
Radiations splitted into 3 parts
Fleming’s Left Hand Rule Dr. Pius Augustine, SH College, Kochi

Range of α – particles
The distance traveled within the medium before it
gets stopped or loses ionizing power completely
is called the range of the alpha particle in the
medium
Range depends on the nature of medium,
pressure, ionization potential of the gas and
initial energy of alpha particle.

A radioactive sample emit either an alpha or a beta at a
time along with gamma radiation.
How will you account for the formation of three dots on
the photographic plate ?
One radioactive nucleus undergoes a series of decays one after
the other, will have different emissions, until a stable end product
is formed.
So many nuclei will do the same
Along alpha or beta emission will be followed by gamma emission
by the excited daughter nucleus

Nucleus of an atom does not contain electron. How will
you account emission of electron (beta) from nucleus?
Two possibilities
Neutron changes to p, e- and antineutrino or proton
changes to neutron, e+ and neutrino
Accordingly, β- or β+ will be emitted from the nucleus.

Properties of α, β and γ
radiations

Sl.
No.
PROPE
RTY
α- PARTICLE β-PARTICLE γ - RAYS
1. Identifi
cation
Nuclei of He4 Fast moving e- Electromagnetic
waves of short
wavelength
2. Electric
charge
Positive
charge(+2e)
Negative
charge(-e)
No charge
3. Rest
mass
Equal to that of He4
nucleus
Equal to rest
mass of
electrons
Zero rest mass
4. Speed About (1/10)th
velocity of light (C)
0.99 c Equal to c

5.
Penetrating
power
Smaller than
that of β –
particle
100 times that
of α- particle
100 times that
of β –particle
6.
Ionizing
power
Higher than
that of β –
particle
(1/100)th of
that of
α- particle
(1/100)th of
that of β –
particle
7.
Behavior in E
and B fields
Deflected in
electric and
magnetic fields
Deflected Not deflected
(electromagn
etic)
8.
Photographic
plate
Affect
photographic
plate
Affect Affect
9. Fluorescence
Produce
fluorescence
Produce Produce

What is the nature of alpha, beta and gamma
radiations? State four properties of each.
Refer previous slides
An alpha particle captures an electron.
What does it change to ?
Singly ionized helium He+

Which radiation suffer maximum deflection
in magnetic field?
Ans: β (lowest mass)
State one difference between a chemical change
and a nuclear change.
Chemical change – due to change in orbital electrons.
Nuclear – change in nucleons inside nucleus.

State the penetrating range of α ,β and γ
α – 2.7 cm to 8.62 cm of air
β – 5mm of Al or 1mm of Pb
γ – 30cm of iron

How do IR and gamma rays differ in wavelength
and penetrating power?
Both are em radiations
Wavelength of gamma rays is much shorter (10-13
m aprox) and IR(10-6 m aprox)
IR is heat rays
Gamma rays are high energetic and much more
penetrating

Electromagnetic Spectrum
Gamma rays-extremity of the spectrum, have high-energy
photons.
High penetrating power
Can ionize other atoms
Very dangerous if you are directly exposed to them.Dr. Pius Augustine, SH College, Kochi

Why do we usually use isotopes emitting gamma
radiations as radioactive tracers (diagnose brain
tumours, blood clots)in medical use?
Gamma radiations are most penetrating (high
energetic)
Why are alpha particles not used in radio therapy ?
Penetrating power is very low and cannot
penetrate through human skin.

State two similarities and two
dissimilarities between the γ rays and X
rays
Similarities : i. both are em radiations.
ii. Equal velocity in vacuum
Dis : i. wavelength difference
ii. γ is higher penetrating than X

State three properties common to beta
and cathode rays
i. Negative charge
ii. Deflected by E and B
iii. Cause fluorescence

State three properties which are
different for beta and cathode rays
i. Cathode rays are extranuclear electrons.
Beta comes from nucleus
ii. Velocity of cathode ray depend on p.d
between anode and cathode (beta rays very
high depending on the source nucleus)
iii. Cathode rays - mass constant, beta –
relativistic variation of mass

92U238 decays to 82Pb206. How many α and β
particles are emitted ?
238 – 206 = 32 [reduction in A]
92 – 82 = 10 [reduction in Z]
No. of α = 32 / 4 = 8
Corresponding reduction in Z is 16.
But given case - only 10. (difference is 6
compensated by β )
No. of β = 6Dr. Pius Augustine, SH College, Kochi

90Th234 decays to 82Pb206 . Find number of
alpha and beta particles emitted ?
Ans: 7α and 6β

A radioactive sample is kept at the centre of large evacuated
sphere. How safe will it be?
What changes do you suggest for more safety ?
α – less penetrating and may be stopped by walls.
β – since evacuated, no absorption within. No. of beta
reaching surface/ area will be minimum if area is large.
γ - thick lead walls will be good to absorb.
(ie. safety - large lead sphere should be used, should
not be evacuated)

A mass of lead is embeded in a block of wood.
Radiations from a radioactive source incident on the side
of block produce a shadow on a fluorescent screen
placed beyond the block. The shadow of wood is faint ,
that of lead is dark. Explain.
If block of wood is replaced by a block of Al, will there be
any change in the shadow?
Wood blocks only alpha.
Lead stops all the three radiations. Hence dark.
Al or light metal will not stop gamma , hence shadow will
be faint.

Radio activity is a nuclear phenomenon.
comment
Emission of radiation from a fixed mass of radioactive
substance is unaffected by chemical change or
physical change like heating ,cooling, finely dividing
etc.
ie. electrons outside nucleus has no role in radioactivity
or it is nuclear phenomenon.

Parent nuclei and Daughter nuclei
A nucleus which undergo radioactive
disintegration is called parent nucleus and
the product nucleus formed is called
daughter nucleus

Alpha Decay
All nuclei with A>210 undergoes alpha decay.
Nucleus will be unstable due to Coulomb repulsive force
α-emission cause reduction in mass number and moves to
stability

Nuclei which are unstable due to low B.E/ nucleon
• To achieve greater stability by reducing size
• Emit alpha which has a high value of binding
energy
• When alpha particles are emitted the B.E/
nucleon increases
• Becomes more stable.

Q-value of nuclear decay or reactions
The difference between the rest mass energy of the
initial constituents (Ui) and that of the final products
(Uf) is called Q-value of the process.
Q = Ui – Uf.
Applicable for any type of nuclear reactions
Alpha decay
Q = [m(zXA) – m(z-2YA-4) – m(2He4)]c2

Beta Decay
unstable due to higher or lower neutron to
proton ratio, than that of a stable nucleus.
Emits β-particles and thus the neutron to proton
ratio is decreased. Dr. Pius Augustine, SH College, Kochi

No electron in the nucleus. How will you account
for β emission ?
Neutron is converted into a proton and an electron.
When a parent nucleus X emits a β-particle, the
daughter nucleus produced will have the same mass
number but the atomic number will be increased by 1
0n1 → 1p1 + -1eo + υ

β – decay and neutrino theory
β emission can be represented as,
z X A  z+1 Y A + -1 e 0 + Q
where Q is the energy released.
According to this eqn, all β particles emitted must have
same energy
Magnetic spectrograph study shows continuous β –
spectrum (energy ranging from 0 to a max ?).
Max energy of spectrum is characteristic of the
radioactive atom emitting β Dr. Pius Augustine, SH College, Kochi

β - spectrum

β – spectrum and confusions ???
1. All particles from a particular radioactive sample
should emit β particles having same energy. But
only a few β particles are emitted with the maximum
value of energy. What about remaining energy?

β – spectrum and confusions ???
2. Conservation of angular momentum . How ?
How is it possible for a nucleus of even mass
number and therefore integral spin give daughter of
same mass and integral spin and emit electron of
spin ½ h/2π ? (Similarily for odd nuclei)
3. Also apparent failure of coservation linear
momentum? Dr. Pius Augustine, SH College, Kochi

β – spectrum and neutrino theory
In 1930 Pauli proposed that if an uncharged
particle of zero mass and spin ½ is emitted
in β – decay together with electron, above
discrepancies can be settled.
Particle was named neutrino.
(which carries difference in energy)
Two type of β (negatron and positron) and hence
neutrino and antineutino.

Neutrino is lacking charge and mass
Neutrino is not electromagnetic in nature
Neutrino can pass unimpeded through vast
amounts of matter.
Neutrino has to pass through over 100 light years of
solid iron on the average before interacting. (can
pass through earth)

Neutrino theory – by Fermi
Both β and neutrino are created in the nucleus
and ejected simultaneously
Total energy of these particles is a constant,
which is the end point energy observed in the
spectrum.

Neutrino theory – by Fermi
β carry max energy when energy of the neutrino
is zero, and other cases less than maximum
Total energy may be shared in any proportion
which is the reason for continuous spectrum

Q-value for beta decay
In beta decay N/Z ratio will be altered
If parent nucleus is having higher number of neutrons,
then neutron will be converted into proton or vice
versa, to move to stability.
This is possible through weak nuclear interactions
associated with beta decay

β- decay
z XA
z+1YA + β- + ν
Q = Ui-Uf = [m(zXA) – m(z+1YA)]c2
Note that rest mass energy of the created electron (β-)
is not subtracted here.
Because of the large mass, the residual nucleus (z+1YA)
will not share appreciable kinetic energy.
So energy is shared between antineutrino and beta
particle (beta spectrum)

β+ decay
z XA
z+1YA + β+ + ν
Q = Ui-Uf = [m(zXA) – m(z-1YA) – 2me]c2
Can an isolated proton decay to a neutron emitting a positron
and a neutrino?
Mass of neutron is larger than the mass of a proton and hence the
Q-value will be negative.
So an isolated proton will not. (inside nucleus, it would be
possible, as there is associated mass variations of the rest of the
particles)
An isolated neutron can. Dr. Pius Augustine, SH College, Kochi

Electron capture
z XA + e z-1YA + ν
Q = Ui-Uf = [m(zXA) – m(z-1YA)]c2
When an electron is captured, vacancy will be filled from
outer electrons and an X-ray photon will be emitted
following the electron capture.

Nucleus can exist in different energy states.
When a radioactive nucleus emits and α-particle or a β-
particle, after the emission, the nucleus will be in the
excited state.
The nucleus can return to the ground state by the
emitting γ-rays, which are e.m. waves of short wavelength.
For example 27Co66 emits a β-particle and is converted to
28Ni60 which is in excited state. 28Ni60 returns to it’s ground
state by emitting two γ-rays.
Gamma Decay

A daughter nucleus formed after α or β decay may
not be stable. More decay may continue until a
stable end product is formed.
α, β and γ dacays are collectively called radioactive
decay and the materials capable of undergoing
radioactive decay are called radioactive material.
α, β and γ are collectively called nuclear radiations.

How much energy is released in the following reaction?
7Li + p α + α
Atomic mass of 7Li = 7.0160 u 4He = 4.0026 u
Energy released = 7Li + p - 2α
= 7.0160 u + 1.007825 u - 2 x 4.0026 u
= 16.83 Mev

Does a nucleus loose mass when it suffers
gamma decay?
In beta decay, an electron or a positron is emitted
by a nucleus. Does the remaining atom get
oppositely charged?

Gamma-ray burst (GRB) is a high-energy explosion that occurs
in space.
Most powerful blasts in the cosmos, and the dazzling flash of
gamma rays fills up our sky at least once every day.
An artist’s illustration of a gamma-ray burst

Energy for Earthquakes comes
from radioactive energy in Earth's mantle.
Radioactive decay produces heat that causes
convection in the mantle.
When the rock breaks, the stored energy is released
suddenly.
This energy is then carried outwards from the break
by seismic waves, a form of energy radiation.
Radioactivity and earthquake?

A combined analysis of the concentrations of radon and
one of its radioactive isotopes called “thoron” may
potentially allow for the prediction of impending
earthquakes, without interference from other
environmental processes, according to new work done
by researchers from Korea.
Radioactivity and earthquake-holy grail of
geophysics?

In radioactive transformations either an alpha or beta particle
is emitted by the atom at one time. Never both or more than
one.
When a radioactive atom emits an alpha particle, the mass no.
of the new element will be less by 4 units and atomic no. less
by 2 units than those of the parent atom.
When a radioactive atom emits a beta particle, the new atom
formed has the same mass no. but the atomic no. increases by 1
Soddy Fajan’s Displacement Law

Radioactive decay law states that the probability per
unit time that a nucleus will decay is a constant,
independent of time.
The radioactive decay of certain number of atoms
(mass) is exponential in time.
It is a universal law – describes statistical behavior of
large number of nuclides.
Radioactive decay law or Rutherford and soddy theory

Radioactive decay law or Rutherford and soddy theory
States that rate of disintegration is directly proportional
to the total number of atoms present at that time.
Consider a sample contains N un decayed nuclei.
Let dN nuclei disintegrate in dt second.
dN/dt α – N
-ve sign signifies that number of nuclei decreases
with time

dN/dt = -λN dN/N = -λdt
Let at time t = 0, no. of undecayed nuclei be N0.and at
time t, no. is N
∫ dN/N = -λ ∫ dt
logeN – logeNo = – λt.
Loge(N/No) = – λt.
N = No e-λt
N0
N
0
t

Time →
↑
N

Definition for decay constant
dN/dt = -λN λ = -dN/dt
N
Decay constant of a radioactive substance is defined as the
ratio of its instantaneous rate of disintegration to the
number of atoms present (N = No e-λt )at that time .
If t = 1/λ, N = No e-λ1/λ = No/e
= No/ 2.718 = 0.368 No.
Radio active decay constant λ may be defined as the
reciprocal of time when the number of atoms of radioactive
substance decreases to 0.368 of the number present

Half life T1/2
Time at which undecayed nuclei falls to half of its
original number.
T = T1/2 N = No/2
N = No e-λt Loge(N/No) = – λt.
loge No/2No = -λ T1/2
loge 2 =λ T1/2
T1/2 = 0.693 /λ
Half life of some elements are shorter than 10-15s and
some as long as 1010years ≈ age of universeDr. Pius Augustine, SH College, Kochi

Half life T1/2
loge 2 =λ T1/2 λ = loge 2/T1/2
T1/2 = 0.693 /λ
N = No e-(log 2/T1/2)t = No e-(log 2)(t/T1/2)
= No = No
e(log 2)(t/T1/2) 2(t/T1/2)
Following the same argument
Activity at time t will be A = Ao
2(t/T1/2)

Radioactive 131I has a half life of 8.0 days. A sample
containing 131I has activity 20μCi at t = 0. a)what is its
activity at t = 4.0 days? b) what is its decay constant at
t = 4.0 days.
a) t = 4.0 days λ = 0.693/T1/2 A0 = 20 x 10-6 Ci
Activity A =Ao e-λt = 14 μ Ci
b) λ = 0.693/T1/2 = λ = 0.693/(8 x 24 x 3600)
= 1.0026 x 10-6

The half life of a radioactive nuclide is 20 hrs.
What fraction of original activity will remain after
40 hrs?
t/T1/2 = 40 hr/20hr = 2
A = Ao
2(t/T1/2)
A/A0 = 1/22

Average or Mean life τ
The mean of the ages of the atoms of the radioactive
element is called average or mean life it is equivalent
to reciprocal of decay constant λ.
τ = Total lives of all the atoms
Total no. of atoms
τ = 1 / λ T1/2 = 0.693 /λ
= T1/2 / loge2 = T1/2 /0.693
= 1.44 T1/2

Mean life τ = τ1 + τ3 + ... + τ2 / n
Where τ1, τ2,....... τn represent the observed lifetime of
the individual nuclei and n is a very large number.
Calculated as a weighted average:
τ = (τ1N1 + τ3N2 + ... + τ2Nn) / (N1 + ... + Nn)
Where N1 nuclei live for time τ1,
N2 nuclei live for time τ2....... and so on.

T1/2 = τ 0.693
T1/2 and τ vary drastically for different substances.
Eg. T1/2 of Po212 is less than 1 μs, while for Th232, T1/2 it is more
than 1 billion years.

Let N0 be the total no. of radioactive atoms in the
beginning and N after a time t.
Let dN disintegrate between t and t+δt.
(if δt is very small , each of these atoms had a life of t)
Total life of dN atoms = (dN)t
Total life of No atoms T = ∫t(dN)
0
∞

Total life of No atoms T = ∫t(dN)
N = No e-λt
dN/dt = λNoe-λt omitting –ve sign as it merely
indicates the decrease
dN = Noe-λt dt (-λ)
Mean life = τ = T/N0. = λ∫ te-λt dt
Integrate by parts will give result τ = 1/λ
0
∞
0
∞

Using calculus
|dN| = λN0e–λtdt
Mean life τ=
1/λ.

Cascade Decays: A nucleus ‘A’ decays into another
nucleus ‘B’, which again decays into ‘C’, and so on until
the series ends in a stable nuclide.
These are known as cascade decays.

Activity of radioactive substance
Is the rate of decay of the nucleus.
If N is the number of radioactive nuclei present in a
sample, out of which a small fraction dN decays in a
small interval dt,
Activity A = -dN/dt =λN
= λ No e-λt = Ao e-λt

Units of Activity
SI unit – Becquerel (Bq)
1Bq = 1 disintegration /second(small unit)
Activity of a radioactive sample is said to be 1Bq , if it
undergoes one disintegration in 1sec.
Non SI units
1 curie (Ci) = 3.7 x 1010 Bq (number of disintegrations
that one gram of radium-226 will undergo in one second.)
1Ci = 37 GBq. (is the activity of 1g radium)
1Rutherford (Rd) = 106 Bq. Dr. Pius Augustine, SH College, Kochi

The decay constant of a radioactive nuclide 64Cu is
1.516 x 10-5 s-1. Find the activity of a sample containing
1 μg of 64Cu. Atomic weight of copper = 63.5g/mole.
Neglect the mass difference between the given
radioisotopes and normal copper.
63.5 g of copper has 6 x 1023 atoms.
(N)No. of atoms in 1 μg of 64Cu ? = 9.45 x1015.
Activity = λN = 1.43 x 1011 disintegrations/sec
1.43 x 1011/3.7 x 1010 = 3.86 Ci

A measure of radioactivity (activity) is based on
counting of disintegrations per second.
The SI unit of activity is the becquerel (Bq),
equal to one reciprocal second.
Activity depends on the number of decays per
second.
Independent of type of decay, the energy of the
decay products, or the biological effects of the
radiation. Dr. Pius Augustine, SH College, Kochi

Specific activity is the activity per quantity
of a radionuclide, (activity per quantity of
atoms) of a particular radionuclide.
It is usually given in units of Bq/g or Ci/g.

Isotopes of elements with atomic number less than 82,
which are radio active are called radioisotopes.
They are prepared artificially.
Artificial radioactivity was discovered by I.Curie and
F.Joliot.
Eg. 27Co60, 6C14 , 19K40, 15P32
Radioisotopes

Al after bombarding with α particles showed
continuous emission of radiations. (even after
source of alpha particles was taken away).
2He4 + 13Al27 → 15P30 + on1
15P30 → 14Si30 + 1e0
Radio active phosphorous differ from the
normal phosphorous only in the mode of
preparation
Such isotopes prepared artificially and are
radioactive are called radioisotopes.

1. They are chemically identical with stable isotope.
Eg.11Na23 and 11Na24 are identical in chemical process. No one
can distinguish, if 11Na24 is in dining table salt.
2. They can be easily detected
11Na24 is β emitter and its progress in the system can be
detected. Thus role of stable isotope can be traced by the
presence of radio isotope.
3. The masses of even small amount of radioisotopes may
be accurately determined.
Properties of radioisotopes which make them useful

Radioactive tracers
In this process an atom in a chemical compound
is replaced by another atom, of the same
chemical element.
This process is often called radioactive labeling.
Used because, radioactive decay is much more
energetic than chemical reactions.

Tracer technique or tagging
Process of deliberately adding a small
quantity of radio isotope with the
substance to be investigated and tracing
the path of radio isotope by means of
radioactive detector is known as tracer
technique.
Used in medicine and agriculture

Medical
i. radiation therapy (Co-60 ) - to kill cells in a tumour
(inhibition of growth)
ii. Diagnosis (radio Nacl, radio Fe, radio I) - used as
tracers to detect suspected brain tumour and blood
clots before become dangerous.
iii. Radio cardiology (radio Nacl) to test blood
circulation
iv. Sterilisation (gamma rays)
Uses of Radioisotopes

27Co60 emits a β – particle and
transforms into 28Ni60 which in turn
emits a gamma radiation (energy 1.17
MeV ) which is used in the treatment of
cancer.
Cobalt therapy

Radio iodine for goitre treatment

I131 has half life 8 days.
If fed to a patient, carried by blood and
collected by thyroid.
Rate at which it is collected can be detected
by radiation detectors.
Rate of accumulation depend on the
condition of the gland.

Scientific
i. Projectiles for nuclear reactions (α).
ii. Radioactive tracers in agriculture
iii. Age of rocks, fossils (Carbon dating)

Industrial
i. Locate obstruction in gas, oil or water pipes
ii. Control the thickness of paper, plastic sheet
etc (manufacture)
iii. Radiography : γ from Co60 used to Check
crack in welding, pipes etc.

Radio carbon dating
When a plant is alive, though C14 present in it
decays, ratio of C14 to C12 remains constant due
to the uptake from atmosphere.
When plant dies C14 start disintegration and ratio
decreases with time exponentially.
By noting the % of C14 in a sample age can be
determined (half life of C14 = 5760 years)

Rock dating
Half life of U238 – 5 x 109 years
End product of series is Pb.(intermediate
elements have short lives)
In a rock after billions of years only major elements
present in appreciable quantity will be U238 and Pb.
Relative proportion of the two in a sample
enables to estimate how long back the rock
contained only U238, gives age of rock.

Radiation measurement – 3 types
i. Source activity – curie (Ci) = 37GBq.
ii. Exposure - rontgen ( R) : one R is the
quantity or exposure of radiation that produce
1.61 x 1015 ion pairs in 1kg of dry air at STP.
iii. Absorbed dose(rad): one rad is that amount
of radiation absorbed in a material which
increases its energy by 0.01joule /kg.

rad / day
0 - 25
25 – 50
50 - 100
100 – 200
200 – 400
400 – 600
600 and
more.
Effect
No observable effect.
Possibility of slight blood changes.
Vomiting, fatigue, loss of apetite,
moderate blood changes etc.
Vomiting, severe blood changes
accompanied by hemorrhage etc
Chances of permanent damage in the
body
50% chance of death. Survivors to suffer
permanent damage.
100% death !!!.......

Biological effects of nuclear radiations – 2 types
1. Somatic effects. (short term recoverable
and long term irrecoverable)
2. Genetic effects (later generations)
Radioactive radiations (α, β and γ) cause
ionization and excitation of atoms of
living cells due to which living cells are
altered or destroyed. Dr. Pius Augustine, SH College, Kochi

Safety precautions at Nuclear plants.
i. Reactors in thick concrete walls to prevent gamma
or neutrons.
ii. Nuclear materials in thick lead containers with
narrow mouth (plug).
iii. Lead lined aprons and gloves.
iv. Handle with mechanical tongs.
v. Wear badges and periodic checking.
vi. Periodic compulsory check up

An object can be seen with a signal if the wavelength of the
wave is smaller than the size of the object.
If not wave will bent around the edge.
Wavelength of electron wave depends on the velocity of
the electron. Higher the velocity lower the wavelength.
Hope you will be able to answer the opening question now.

For my youtube videos: please visit -
SH vision youtube channel
or
xray diffraction series
SH Vision
Dr. Pius Augustine, SH College, KochiDr. Pius Augustine, SH College, Kochi

160
Appeal: Please Contribute to Prime Minister’s or Chief
Minister’s fund in the fight against COVID-19
Dr. Pius Augustine, Dept of Physics, Sacred Heart College, Thevara
we will
overcome
Thank You
http://piusaugustine.shcollege.ac.in
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Dr. Pius Augustine, Asst. Professor, Sacred Heart College, Thevara, Kochi.

26 pius augustine nucleus and radioactivity

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