Half life of radioactive sample undergoing alpha decay is `1.4`x`10^17s`. If number of nuclei in sample is `2.0`x`10^21` activity of sample is nearly

Options

A. `10^4 Bq`
B. `10^5Bq`
C. `10^6Bq`
D. `10^3`Bq`

Answer

To solve the problem, we need to calculate the activity of a radioactive sample undergoing alpha decay using the given half-life and the number of nuclei in the sample.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Half-life (T_half) = \(1.4 \times 10^{17} \, \text{s}\)
- Number of nuclei (N) = \(2.0 \times 10^{21}\)

2. **Calculate the Decay Constant (λ):**
The decay constant (λ) can be calculated using the formula:
\[ \lambda = \frac{\ln(2)}{T_{1/2}} \]
Where \(\ln(2) \approx 0.693\).

Substituting the values:
\[ \lambda = \frac{0.693}{1.4 \times 10^{17}} \approx 4.95 \times 10^{-18} \, \text{s}^{-1} \]

3. **Calculate the Activity (A):**
The activity (A) of a radioactive sample is given by the formula:
\[ A = \lambda N \]
Substituting the values of λ and N:
\[ A = (4.95 \times 10^{-18} \, \text{s}^{-1}) \times (2.0 \times 10^{21}) \]

Performing the multiplication:
\[ A \approx 9.9 \times 10^{3} \, \text{Becquerel} \]

Rounding this gives:
\[ A \approx 10^{4} \, \text{Becquerel} \]

4. **Final Answer:**
The activity of the sample is approximately \(10^{4} \, \text{Becquerel}\).