GATE-2018 (24) :Wyllie – Time average equation

GATE-2007

63.After decaying through 7 half-life periods , the original amount of radioactive substance that reduces to an amount of 1/64g is,

A) 0.25 g             B) 0.50 g              C) 1.0g              D) 2.0g

Solution:

If ‘N’ is the amount of substance remained after ‘t’ half lifes of a substance N₀ are related by,

$\frac{N}{N_{0}}=(\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}}$--(1)

$t =7t_{\frac{1}{2}}$

$N =\frac{1}{64}$

$N_{0}$=?

Substitute the above values in the eq(1)

$\frac{1}{64_{N_{0}}}=\frac{1}{2}^{\frac{7t_{\frac{1}{2}}}{t\frac{1}{2}}}$

$\frac{1}{64N_{0}}=2^{-7}$

$2^{7}=64N_{0}$

$N_{0}=\frac{2^{7}}{2^{6}}$

$N_{0}=2^{7-6}$

$N_{0}=2grams$