Nucleus - 3

Radioactive decay process follows first order Kinetics i.e rate of reaction depends upon no. of nucleus raised to power one. where disintegration / decay constant.
or
Integrating both sides


for half life N = N₀/2


Activity of a radioactive substance is the rate of decay or the number disintegration per second . it is denoted by A.

Also A = A₀ where A₀ initial activity.

Dumb Question:
Why has the rate been taken as negative of rate of change of no. of nuclei
Ans:- It is known that in a radioactive decay, the no. of nucleii always decreases,
itself will be negative, so to get overall rate as a positive quantity R = -
• no. of nucleii remaining after n half lives is given by
N =

Illustration:-
Uranium areas on the earth at present time typically have a composition consisting of 99.3% of the isotope ₉₂U²³⁵ and 0.7% of the isotope ₉₂U²³⁵. The half lives of those isotopes are 4.47 x 10⁹y and 7.04 x 10⁸y respectively. if then isotopes were equally abundant when the earth was formed, estimate the age of earth
Solution:- let no be number of atoms of each isotope at the time of formation of the earth (T = 0) and N₁ and N₂ the number of atoms at present(t - t) then
N₁ = N₀ ………………………………………………………..(i)
N² = N₀ ………………………………………………………..(ii)

Further it is given that
Equating (iii) and (iv) and taking log on both sides, we have

Substituting the values, we have


(1) Graphical Representation:- Since the radioactive decay process follows experential rate law hence
it has graph as shown in adjacent figure.