Nuclei - Result Question 65

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66. A mixture consists of two radioactive materials $A_1$ and $A_2$ with half lives of $20 s$ and $10 s$ respectively. Initially the mixture has $40 g$ of $A_1$ and $160 g$ of $A_2$. The amount of the two in the mixture will become equal after :

======= ####66. A mixture consists of two radioactive materials $A_1$ and $A_2$ with half lives of $20 s$ and $10 s$ respectively. Initially the mixture has $40 g$ of $A_1$ and $160 g$ of $A_2$. The amount of the two in the mixture will become equal after :

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/nuclei/nuclei—result-question-65.md (a) $60 s$

(b) $80 s$

(c) $20 s$

(d) $40 s$

[2012]

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Answer:

Correct Answer: 66. (d)

Solution:

  1. (d) Let, the amount of the two in the mixture will become equal after $t$ years.

The amount of $A_1$, which remains after $t$ years

$N_1=\frac{N _{01}}{(2)^{t / 20}}$

The amount of $A_2$, which remains, after $t$ years

$N_2=\frac{N _{02}}{(2)^{t / 10}}$

According to the problem

$N_1=N_2$

$\frac{40}{(2)^{t / 20}}=\frac{160}{(2)^{t / 10}}$

$2^{t / 20}=2^{(\frac{t}{10}-2)}$

$\frac{t}{20}=\frac{t}{10}-2$

$\frac{t}{20}-\frac{t}{10}=2$

$\frac{t}{20}=2$

$t=40 s$