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 nuciei will be:

• A. 4:1
• B. 1:4
• C. 5:4
• D. 1:16

Answer 1

The correct option is C

5:4

$T_{\frac{1}{2}}$ of A=20 minutes

$T_{\frac{1}{2}}$ of B=40 minutes

After 80 minutes

$\frac{N_A\left(Decayed\right)}{N_0}=1-(\frac{1}{2}{)}^4$………(1)

$\frac{N_B\left(Decayed\right)}{N_0}=1-(\frac{1}{2}{)}^2$………(2)

$\frac{N_A}{N_B}=\frac{5}{4}$