Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be :

Question

Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be : (A) 1: 16 (B) 4: 1 (C) 1: 4 (D) 5: 4

Tardigrade Admin · Accepted Answer

beginarrayl n = n 0 e -α t α A = ln 2 / 20 α B = ln 2 / 40 endarray After 80 min, remaining number of nuclei for A , n A = n o / 16 After 80 min, remaining number of nuclei for B, nB=n0 / 4 Decayed number of nuclei for A , Δ n A =(15/16) n O Decayed number of nuclei for B , Δ n B =(3/4) n O Ratio of decayed number of nuclei is (Δ n A /Δ n B )=(15 / 16/3 / 4)=5: 4

Q. Half-lives of two radioactive elements $A$ and $B$ are $20$ minutes and $40$ minutes, respectively. Initially, the samples have equal number of nuclei. After $80$ minutes, the ratio of decayed numbers of $A$ and $B$ nuclei will be :

$1 : 16$

$4 : 1$

$1 : 4$

$5 : 4$

Q. Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be :

1:16

4:1

1:4

5:4

Q. Half-lives of two radioactive elements $A$ and $B$ are $20$ minutes and $40$ minutes, respectively. Initially, the samples have equal number of nuclei. After $80$ minutes, the ratio of decayed numbers of $A$ and $B$ nuclei will be :

$1 : 16$

$4 : 1$

$1 : 4$

$5 : 4$