BITSAT 2022 Paper

From radioactive decay law,
−

dN

dt

∝N‌or−

dN

dt

=λN
Thus, A=−

dN

dt

‌or‌A=λN
⇒A=λN0e−λt .......(i)
Where, A0=λN0 is the activity of the radioactive material at time, t=0
At time, t1.......A1=A0e−λt1..(ii)
At time, t2.......A2=A0e−λt2........(iii)
On didviding Eq. (ii) by Eq. (iii), we have

A1

A2

=

e−λt1

e−λt2

=e−λ(t1−t2)
⇒A1=A2e−λ(t1−t2)