SATHEE: Modern Physics 3 Question 6

Modern Physics 3 Question 6

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

(2016 Main)

(a) $1 : 16$

(b) $4 : 1$

(d) $5 : 4$

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Solution:

A : Numbers left : $N \to \frac{N}{2} \to \frac{N}{4} \to \frac{N}{8} \to \frac{N}{16}$

$∴$ Number decayed, $N_{A} = N - \frac{N}{16} = \frac{15}{16} N$

B : Numbers left : $N \to \frac{N}{2} \to \frac{N}{4}$ $∴$ Numbers decayed, $N_{B} = N - \frac{N}{4} = \frac{3}{4} N$

Ratio :

$\frac{N_{A}}{N_{B}} = \frac{(15 / 16) N}{(3 / 4) N} = \frac{5}{4}$

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Modern Physics 3 Question 6

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

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