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7.

Radioactivity

Properties of a, b particles and g rays:

Property

a

b

g

1.

Charge

+2e

- e

0

2.

Mass

- 4m_{p} where m_{p} = mass of proton

m_{e} where m_{e} = mass of electron

Radiation

3.

Speed when emitted

10^{7} m/s

Upto 99% of c

c

4.

Ionization of gas/air

Intense

Moderate

Low

5.

Penetrating Power

Least

Highest

6.

Deflection by

Deflected

Not deflected

Change in Z, A of emitting nucleus

A ® A - 4 Z ® Z - 2

Z ® Z + 1

No change

8.

Photographic plate

Affect

9.

Produce fluorescence?

Yes

c : speed of light

Rutherford-Soddy Laws or Group Displacement Laws:

(Laws of radioactive transformation)

Law of Radioactive Decay

Statement: The rate of radioactive disintegration at any instant is directly proportional to the number of radioactive nuclei of the parent element present at that time.

dN

a N

dt

\

= - lN

where l is a constant called the decay constant. Negative sign indicates that as time increases, no. of atoms decreases.

Integrating the equation

= - lN, we get,

N = N_{0} e ^{-}^{l}^{t}

This expression is called exponential law of radioactive decay.

Graph:

This graph shows the variation of the number of radioactive atoms (N) with time t. Further, it shows that law of decay is exponential in nature.

Half Life

Half life (T) of a radioactive element is defined as the time required for half the initial number of radioactive nuclei of the element to disintegrate.

i.e. N =

N_{0}

at t = T (half life)

2

Using this in the equation N = N_{0} e ^{-}^{l}^{t} we get,

T

=

0.693

l

t = 0 No. of atoms = N_{0} = N_{0}/2^{0}

t = T

= N_{0}/2^{1}

t = 2T

= N_{0}/2^{2}

4

t = 3T

= N_{0}/2^{3}

8

\ t = nT

N =

2^{n}

= 2^{n}

, when t = nT

N

Decay Constant l = -

dN/ N

Hence the decay constant l can be defined as the fraction of radioactive nuclei (dN/ N) disintegrating per unit time. The SI unit of l is (second)^{-}^{1}.

l is a measure of stability of a radioactive material.