CGPET 2021 Solved Paper

Given, initial number of nuclei =N0
After time t, remaining number of nuclei,
N=N0e−λt(where,λ=decay‌constant)
Given, at time, t=0
For radioactive substance A,
NA=N0e−5λt
Similarly, for B,
NB=N0e−λt
∴ Ratio

NA

NB

=

N0e5−λt

N0e−λt

=

e−5λt

e−λt

⇒

NA

NB

=e−4λt .....(i)
It is given that after time t,
the ratio,

NA

NB

=(

1

2

)2......(ii)
From Eqs. (i) and (ii), we get
⇒ (

I

e

)2=e−4λt⇒e−2=e−λ
Comparing the powers, we get −2=−4λt⇒t=

I

2λ

Hence, the ratio of number of nuclei of A to those of B will be (

I

e

)2 after a time of

I

2λ

∴ No option in the given question is correct