Question

$1g$ of a radioactive substance disintegrates at the rate of $3.7\times {10}^{10}$ disintegration per second. The atomic mass of the substance is $226$. Calculate its mean life.

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

Answer 1

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

We know that the activity $A=\frac{N}{T}$

where $N$ is number of nuclei and $T$ is mean life.

So the mean life $T=\frac{N}{A}=\frac{moles\times 6.02\times {10}^{23}}{3.7\times {10}^{10}}$ ...............(1)

putting $moles=\frac{1gram}{226gram/mole}=0.00442$ in eqaution-1

we get $T=7.194\times {10}^{10}second$