Law of Radioactive decay

Law of radioactive decay: At any instant, the rate of

radioactive disintegration is directly proportional to

the number of nuclei of the radioactive element

present at that instant.

Derivation: Let N0 be the number of nuclei present at

time t = 0 and N the number of nuclei present at

time t.

From the law of radioactive decay, dNN

dt

dNN

dt

dNdt

N …(i)

where, λ is a constant of proportionality called the

radioactive decay constant or the disintegration

constant. It is a constant for a particular radioactive

element. The minus sign indicates that N decreases

as t increases.

Integrating equation (i),

0N t t

0 0 0

dNdt dt

N

∴ loge N – loge N0 = −λt

e0

Nlog t

N

…(ii)

t

0

Ne

N

∴ N = N0 e-λt …(iii)

This is the exponential form of the law of

radioactive decay. It shows that the number of nuclei

present decreases exponentially with time.

Keep on visiting www.ednexa.com

For more information, please call 9011041155.

- Team Ednexa