Rankers Physics

Nucleus: Practice Problem & Solution

The half life of a radioactive sample undergoing $\alpha$-decay is $1.4 \times 10^{17} s$. If the number of nuclei in the sample is $2.0 \times 10^{21}$, the activity of the sample is nearly. (2020-Covid)
$10^5 Bq$
$10^6 Bq$
$10^3 Bq$
$10^4 Bq$

Solution Explained:

To solve this problem, we apply the core principles of Nucleus. Understanding the underlying formula is key to arriving at the correct answer below:

Activity $A = \lambda N = \frac{\ln 2}{T_{1/2}} N$. Substituting the values gives $A \approx \frac{0.693}{1.4 \times 10^{17}} \times 2.0 \times 10^{21} \approx 0.99 \times 10^4 Bq$, which is nearly $10^4 Bq$.

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