Question

$1g$ of radio active substance disintegrates at the rate of $3.7\times {10}^{10}$ disintegrations per second. The atomic mass of the substance is $226$. Calculate its means life.

• A. $1.2\times {10}^{5}s$
• B. $1.39\times {10}^{11}s$
• C. $2.1\times {10}^5$
• D. $7.194\times {10}^{10}S$

Answer 1

The correct option is D $7.194\times {10}^{10}S$

$Moles=1/226=4.4248\times {10}^{-3}$

Atoms$=N=6.02\times {10}^{23}\times 4.4248\times {10}^{-3}=26.637\times {10}^{20}$

As we know that $rate=N/\tau$ where $\tau$ is mean life

so $\tau =N/rate=26.637\times {10}^{20}/(3.7\times {10}^{10})=7.2\times {10}^{10}second$

Option D is correct.