Question

Half-life of a radioactive substance is T. At time t_1 activity of a radioactive substance is R_1 and at time t_2 it is R_2. Find the number of nuclei decayed in this interval of time.

Answer 1

Given:

Half-life of a radioactive substance is T.

Activity of a radioactive substance, at T1 = R1

Activity of a radioactive substance, at T2 = R2

To Find:

the number of nuclei decayed in this interval of time.

Solution:

We know , decay constant ,

• L = 0.693/T

Also, Number of nuclei at a time t , is

• N = No$e^{-Lt}$

Reactivity,

• R = dN/dt =  - LNo$e^{-Lt}$

At t = T1, R = R1

and at t = T2 , R =R2

• R1 = LNo$e^{-LT1}$  = - LN1
• R2 = LNo$e^{-LT2}$ = - LN2

Number of nuclei decayed = Number of nuclei left at t1 - Number of nuclei left at t2

• Ndecay = N1 - N2 = - R1/L - - R2/L = (R2 - R1)T/0.693

The number of nuclei decayed in this interval of time is (R2 - R1)T/0.693.