Atoms And Nuclei Question 402

Question: A radioactive nucleus A with a half-life T, decays into a nucleus B. At t=0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.3. Then, t is given by

Options:

A) t=Tlog(1.3)

B) t=Tlog(1.3)

C) t=Tlog2log1.3

D) t=log1.3log2T

Show Answer

Answer:

Correct Answer: D

Solution:

  • Let initially there are total N0

number of nuclei At time t,NBNA=0.3 (given)
,NB=0.3NA

N0=NA+NB=NA+0.3NA,NA=N01.3

As we know Nt=N0eλt or, N01.3=N0eλt 11.3=eλtln(1.3)=λt

or t=ln(1.3)λ,t=ln(1.3)ln(2)T=ln(1.3)ln(2)T



NCERT Chapter Video Solution

Dual Pane