Question

A sample of a radioactive element containing $4\times {10}^{16}$ active nuclei. If the half-life of the element is $10$ days, then the number of decayed nuclei after $30$ days is:

• A. $0.5\times {10}^{16}$
• B. $2\times {10}^{16}$
• C. $3.5\times {10}^{16}$
• D. $1\times {10}^{16}$

Answer 1

The correct option is C $3.5\times {10}^{16}$

No. of active nuclei present in original sample = $4\times {10}^{16}$

Half-life of element = 10 days.

No. of half-life in 30 days = $\frac{30}{10}=3$

No. of nuclei present after 30 days = $\frac{4\times {10}^{16}}{{\left(2\right)}^3}\Rightarrow 0.5\times {10}^{16}$

No. of decayed nuclei = (No. of active nuclei present originally) - (No. of Active nuclei present after 30 days)

= $4\times {10}^{16}-0.5\times {10}^{16}$