Nuclei - Result Question 86
88. Half-lives of two radioactive substances $A$ and $B$ are respectively 20 minutes and 40 minutes. Initially, the samples of $A$ and $B$ have equal number of nuclei. After 80 minutes the ratio of remaining numbers of $A$ and $B$ nuclei is [1998]
(a) $1: 16$
(b) $4: 1$
(c) $1: 4$
(d) $1: 1$
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Answer:
Correct Answer: 88. (c)
Solution:
- (c) $80=20 \times n_A \Rightarrow n_A=4$
$80=40 \times n_B \Rightarrow n_B=2$
$\frac{N_A}{N_B}=\frac{(\frac{1}{2})^{4}}{(\frac{1}{2})^{2}}=\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}$
