Question

The half-life of ${}^{198}Au$ is 2.7 days. Calculate the decay constant. Take atomic weight of ${}^{198}Au$ to be 198 g $mo{l}^{-1}$.

• A. $2.9\times {10}^{-10}{s}^{-1}$
• B. $2.9\times {10}^{-8}{s}^{-1}$
• C. $2.9\times {10}^{-6}{s}^{-1}$
• D. $2.9\times {10}^{-4}{s}^{-1}$

Answer 1

The correct option is C $2.9\times {10}^{-6}{s}^{-1}$

It’s a simple question. We have been given the value of the half-life and we have to calculate the decay constant.
Let's use the formula which gives us the relation between the two .
$t_{\frac{1}{2}}=\frac{In2}{\lambda }=\frac{0.693}{\lambda }\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{2.7days}=\frac{0.693}{2.7\times 24\times 3600s}=2.9\times {10}^{-6}{s}^{-1}$