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Radioactivity
The spontaneous emission of radiation from unstable heavy nucleus or isotopes of
some elements is called Radioactivity. The elements which emits such radiations
are called radioactive elements.

Radiation emitted by Radioactive elements

The radioactive elements emit 3 different type of radiation. Such radiation is
demonstrated by a simple experiment. A radioactive radium(Ra) source is placed
inside the lead block. A small hole is drilled in a lead block from which a narrow
beam of radiation will emerge out. The nature of radiation is studied by applying
Electric field.

Fig: Emission of radiation

This experiment shows that,
 The component of radiation which bends towards negative plate is called α-
Rays.
 The component of radiation which bends towards positive plate is called β-
Rays.
 The component of radiation which goes straight is called γ-Rays.

Laws of Radioactivity (Radioactive Disintegration)

There are following laws of radioactive disintegration

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1. It is a spontaneous process Which is unaffected by external factors

such as temperature, pressure, electric field, magnetic field etc.
2. Only one of the α or β-particle is emitted at a time. The simultaneous
emission of both the particle is impossible.
3. When α-particle is emitted a new nucleus is formed whose atomic
number decreases by two and mass number decreases by four.
AX → A-4Y α(4He2)
Z z-2 +
parent nucleus daughter nucleus α-particle

4. when β-particle is emitted, a new nucleus is formed whose mass

number remains same but atomic number increases by one.
AX → AY 0e + ̅ν (antineutrino)
Z z+1 + -1
parent nucleus daughter nucleus β-particle

5.
When γ-particle is emitted the newly formed nucleus just goes to
ground state.
A*X → AX
Z Z + γ-rays
Excited nucleus ground state

(These laws are called displacement laws)

6. The rate of disintegration(decay) of radioactive substances (nuclei of
atom) at any instant of time is directly proportional to the number of
atoms present at that time. This is called decay law
Radioactive Decay
Alpha decay: The phenomenon of emission of alpha particle from a radioactive
nucleus is called alpha decay. An alpha ray is a stream of particle that are made of
two protons and two neutrons and are identical to the nuclei of helium nucleus.
When a nucleus undergoes alpha decay its atomic number and mass number are
reduced by 2 and 4 respectively.
α-decay is generally expressed in following ways,

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AX → A-4Y α(4He2)
Z z-2 +
parent nucleus daughter nucleus α-particle

238U → 234Th α(4He2)

92 90 +

Beta decay: The spontaneous emission of β-particle from radioactive nucleus is

called Beta decay. Beta ray is simply a stream of electron.
β-particle ejected from nucleus when a neutron is transformed into proton , i.e.,
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n0 → 1p1 + 0e-1 . Electron cannot exist inside the nucleus, so they are ejected from
nucleus. When a nucleus undergoes beta decay, its mass number remains same but
atomic number increase by one.
β-Decay is generally expressed in following ways
AX → AY 0e - ̅ν (antineutrino)
Z z+1 + -1 (β ) +
parent nucleus daughter nucleus β-particle

14C → 14N 0e - ) + ̅ν (antineutrino)

6 7 + -1 (β )

Gamma Decay: Alpha and beta decays of radioactive nucleus usually leave the
daughter nucleus in an excited state. If the excitation energy available with the
daughter nucleus is not sufficient for further particle emission, it loses its energy
by emitting electromagnetic radiation, also known as γ-rays. when a nucleus
undergoes gamma decay, its atomic mass number and atomic number remains
same.
γ-Decay is generally expressed in following ways,
A*X → AX
Z Z + γ-rays
Excited nucleus ground state

87*Sr → 87Sr
38 38 + γ-rays

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Properties of Radioactive radiation

1. Properties of α-particles
a. α-particles are nuclei of helium atoms9charge (+2e)
b. They are deflected in electric and magnetic fields
c. They affect a photographic plate
d. They have very low penetrating power because they are massive particle. So they
can be stopped by sheet of paper, 0.01 mm thick aluminium foil.
e. They have high ionizing power, greater than both Beta and gamma particle.
f. They produce heating effect when they are stop
2. Properties of β-particle
a. They are negatively charged particles and charge of Beta particle is equal to (-e).
They move with the velocity of 108 m/s
b. They can induce artificial radioactivity
c. They affect a photographic plate
d. They have greater penetrating power than alpha particle and lower penetrating
power than gamma particles.
e. They have less ionizing power than that of Alpha particle.
f. They are deflected in electric and magnetic fields.

3. Properties of γ-rays
a. They are stream of electrically neutral particle called photon.
b. They produce heat on surfaces exposed to them
c. They can produce a nuclear reaction
d. They have greater penetrating power than alpha and gamma particles (It can
pass through 5cm thick sheet of lead and 30 cm thick sheet of iron)
e. They have less ionizing power than that of Alpha particle and Beta particle
f. They are not deflected in electric and magnetic fields.

Cause of Radioactivity:
In a nucleus of an atom, two types of forces are acting there. One is attractive
strong nuclear force between the nucleons and the other is repulsive electrostatic
force between the protons. If attractive force dominates the repulsive force, the
nucleus becomes stable but if repulsive force is too much greater than the

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attractive force, the nucleus becomes unstable. Such unstable nucleus emits
radioactive radiations. Hence, unstable nucleus is the main cause of radioactivity

Radioactive Decay Law:

This law states that “The rate of disintegration(decay) of radioactive substances
(nuclei of atom) at any instant of time is directly proportional to the number of
atoms present at that time”.
Let N be the number of radioactive nuclei present in a radioactive substance at any
instant of time t. Let dN be the number of such nuclei that disintegrates in a short
𝑑𝑁
interval of time dt. Then the rate of disintegration is directly proportional to N.
𝑑𝑡
i.e.

(where λ is decay constant or disintegration constant or transformation constant.

Its value is different for different radioactive substances and the negative sign show
that number of atom decrease as time increase)
from equation (i)

Let N0 be the number of radioactive atoms present at time t=0 and n be the number
of atoms left at time t.
Integrating equation (ii)
𝑵 𝒅𝑵 𝒕
∫𝑵𝟎 = -λ∫𝟎 𝒅𝒕
𝑵

[𝒍𝒏𝑵]NNo = -λ[𝒕]t0

lnN – lnN0 = -λt

𝑵
ln = -λt
𝑵𝒐

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𝐍
= 𝐞−𝛌𝐭
𝐍𝐨

N = N0𝒆−𝝀𝒕

this equation is known as the decay equation, this equation shows that number of
atom fall exponentially with time. N becomes zero only when t approaches infinity.
Therefore, radioactive substance will never disintegrate completely, which is
shown in the graph between number of atoms(N) with time.

Fig: Radioactive decay with time

Decay constant, Half-life and Mean-life:

Decay Constant
from decay law,

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Thus the ratio of the number of disintegration per second to the number of atoms
present in that radioactive substance is called the decay constant.

Also, if we put t=1/λ in decay equation N = Noe-λt ,

We get,
𝟏
−𝝀.𝝀
N = N0 𝒆
N = No . 𝒆−𝟏
𝑵𝒐
N =
𝒆
𝑵𝒐
N =
𝟐.𝟕𝟏𝟖

N = 0.37 No = 37% 0f No.

Hence decay constant may also be defined as the reciprocal of time during which
the number of radioactive atoms of a radioactive substance falls to 37% of its
original value.
Half life
The half-life of a radioactive substance is defined as the time required for ½ of the
radioactive substance to disintegrate. It is denoted by T1/2.
For example, radium-226 has a half life of 1620 years. This means, in the next 1620
years half of the radium will decay, leaving only half of original number of radium
atoms.
Relation between half and decay constant:
𝑵𝒐
In half life period, t = T1/2 and N =
𝟐

We have from decay law

N = No𝒆−𝝀𝒕
𝐍𝐨
Since, At, t = T1/2, N =
𝟐
Then,
𝐍𝐨
𝟐
=N0𝒆−𝝀𝐓𝟏/𝟐

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𝟏
𝒆−𝝀𝐓𝟏/𝟐 = 𝟐
𝒆𝝀𝐓𝟏/𝟐 = 2
λT1/2 = ln2
𝟎.𝟔𝟗𝟑
T1/2 = 𝝀

Hence half time of radioactive substance is inversely proportional to the decay

constant.
Number atoms left after nth Half life:
Let No be the number of radioactive nuclei in a sample specimen in the beginning
of radioactivity.
𝑁𝑜
After time T1/2, the number of atoms left will be =
2
1 𝑁𝑜 1
After 2T1/2, the number of atoms left will be = ( ) =( )2 No
2 2 2
1 1 𝑁𝑜 1
After 3T1/2, the number of atoms left will be = ∗ ( ) =( )3 No
2 2 2 2
Similarly,
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After nT1/2, the number of atoms left will be =( )n No
2
Therefore, number of radioactive atom left after nth half life is,
1
N =( )n No
2

Mean life (Average life):

The ratio of the sum of the life of all atoms to the total number of atoms in the
radioactive element is called mean life or average life of radioactive substance It is
denoted by T or Tmean.
𝒔𝒖𝒎 𝒐𝒇 𝒂𝒈𝒆𝒔 𝒐𝒇 𝒂𝒍𝒍 𝒂𝒕𝒐𝒎𝒔
Tmean =
𝑻𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒂𝒕𝒐𝒎𝒔
𝑵𝒐
( Hints: sum of ages of all atoms = )
𝝀
𝑁𝑜 1
Tmean = .
𝜆 𝑁𝑜

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Tmean =
𝜆

In other words the reciprocal of decay constant is called mean life.

𝑇1/2
Tmean =
0.693

Therefore, Tmean =1.443 T1/2

Thus the mean life of a radioactive substance is longer than its half life.

Activity of Radioactive substance:

The rate of decay of radioactive substance is called the activity A or R of the

substance.
𝑑𝑁
A = = -λN
𝑑𝑡
|A|= λN , A = λN

0.693
A= N
𝑇1\2
So, A α N. If Ao is the activity of a substance at time t=0, then
Ao = λNo
𝐴 𝜆𝑁 Noe−λt
= =
Ao 𝜆No No

A =Ao𝑒 −𝜆𝑡

Radiocarbon dating:
A process to determine the age of geological and archeological objects is called
Radiocarbon dating.
Atmosphere contains carbon 12C6 and its radioactive isotope 14C6. Nitrogen found in
the Atmosphere absorbs a neutron by cosmic rays and forms Radiocarbon.
14N 1n → 14C 1H
7+ 0 6+ 1
The ratio of 14C6 to 12C6 in the atmosphere is about10-12. Both 14C6 and 12C6 combine
with oxygen to form carbon dioxide that is absorbed by the living plants during
photosynthesis process. But 14C6 is a β- emitter and decays back into nitrogen as

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14 14 0
C7 → N7 + e-1
Hence, the amount of 14C6 goes on decaying. As the living plant performs
photosynthesis, the decay of 14C6 is compensated by a new supply of it from
atmospheric air and a radioactive equilibrium is reached where there is a fixed ratio
of14C6 to 12C6.
When the plant dies, no more 14C6 is taken in and that inside the plant begins to
decay at a known rate without any replacement,
Suppose No be the number of radioactive 14C6 atom present in an organism at the
time of death (excluding 12C6), t=0. At time t after its death, the organism contains
N12 and N14 number atoms of 12C6 and 14C6 respectively (due to disintegration of No
number of 14C6). During the time progress, N12 increases and N14 decreases,
however total number of carbon atoms are conserved
No of remaining 14C6 atom(N)=N14
No of initial atoms(N0) = N12+N14 (hints: N12 no of 14C6 atoms decayed)
Age of fossil (t) =?
From radioactive decay equation

N = No𝒆−𝝀𝒕
N14 = (N12 + N14)𝒆−𝝀𝒕
𝐍𝟏𝟒
= 𝒆−𝝀𝒕
𝐍𝟏𝟐 + 𝐍𝟏𝟒
𝐍𝟏𝟐 + 𝐍𝟏𝟒
𝒆𝝀𝒕 =
𝐍𝟏𝟒
𝐍𝟏𝟐 + 𝐍𝟏𝟒
λt = ln( )
𝐍𝟏𝟒
𝟏 𝛌(𝐍𝟏𝟐 + 𝐍𝟏𝟒)
t= ln[ ]
𝝀 𝛌.𝐍𝟏𝟒
𝟏 𝑨𝒐 𝟎.𝟔𝟗𝟑
t = ln( ), But λ =
𝝀 𝑨 𝑻𝟏/𝟐
𝑻𝟏/𝟐 𝑨𝒐
t= ln( )
𝟎.𝟔𝟗𝟑 𝑨

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For radioactive carbon, T1/2 = 5730 years

Hence by measuring the activity A0 of living plant and activity A of its dead material,
the age of that object can be determined.

Radio Isotopes:
The isotopes of an elements which are also radioactive are called radioactive
isotopes or simply radio isotopes. For example,14C, 11C emit radioactive radiation,
they are known as radio isotopes of carbon.

Geiger Muller counter: A Radiation Detector

A Geiger Muller(GM) counter is a device used to detect ionizing particles or nuclear
radiation. It consists of a metal cylinder as the cathode C. A metal wire (central
wire) runs along the axis of cylinder as anode A. the cylinder is filled with a gas such
as argon mixed with halogen vapour at a low pressure of about 10 cm of Hg. The
tube has very thin mica end window W.

Fig: G.M counter

The high tension source (H.T) supplies a potential difference of the
value little than the ionizing potential of the gas through the resistance Ras
shown in above figure.

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When single ionizing particle, like a β- particle or a γ-ray of photon

enters in to the tube through the window W, it will ionize the gas. The P.d.
applied accelerates the ions towards the electrodes which produce more
ions making collision with gas molecules. So, an avalanche of ions is produced
inside the tube which travels towards the electrodes and produce current in
the external resistance R. The resulting drop in potential across r reduces the
potential across the tube below the threshold value and the current decays
rapidly as the circuit has a small time constant. The momentary surge of
current produces an electric pulse which corresponds o one particle entering
the counter. The successive current pulse generated in the resistance R,
corresponding to the number of ionizing particles passing into the tube, are
detected and counted by the counter.
The radioactive particle emitted from a given sample in a given interval
of time can be counted by placing the sample at some distance from the
window

Units of Radioactivity:
The activity of radioactive substance is measured in terms of disintegration per
second.
(i) Curie (Ci): It is defined as the activity of a radioactive substance which
gives 3.7 × 1010 disintegration per second. It is equal to the activity of 1 g
of pure radium
1 Ci = 3.7 × 1010 disintegration/second
(ii) Rutherford (rd): It is defined as the activity of a radioactive substance
which gives 106disintegration per second
1 rd = 106 disintegration/second
(iii) Becquerel (Bq): It is SI-unit of radioactivity
1 Bq = 1 disintegration/second
1 Ci = 3.7 × 1010 disintegration/s =3.7 × 1010 Bq =3.7 × 104 rd

Medical uses of Nuclear reaction and Health Hazards

Medical uses:
1) Radioactive radiations are used in the production and modification of plastics.

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2) Nuclear radiation like γ-rays have been utilized for the preservation of food.
3) Radiation mutation in plants has been practiced to produce new varieties of
these plants.
4) Radio phosphorous is used for treating skin diseases and leukemia.
5) Radio iodine is used to determine the condition of the human thyroid gland.

Possible Health Hazards:

1) The strong α-ray exposure can cause lung cancer.
2) Exposure to fast and slow neutrons can cause blindness.
3) The exposure to neutrons, protons, and α-particles causes damage to RBC.
4) The strong exposures to proton and neutron can cause serious damage to
reproductive organs.

Safety measures or precautions:

1) The worker asked to wear lead aprons.
2) Radioisotopes are handled with the help of a remote control device.
3) Nuclear explosions should carry out far away from the public area.

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