The decay constant λ of a certain radioactive material is 0.2166 per day. The average life τ of the radioactive material is….

Options

A. 5.332 days
B. 4.617days
C. 2.166 days
D. 1.083 days

Answer

To find the average life (τ) of a radioactive material given its decay constant (λ), we can use the relationship between average life and decay constant. The average life is defined as:

\[ \tau = \frac{1}{\lambda} \]

Given that the decay constant \( \lambda \) is 0.2166 per day, we can substitute this value into the formula.

### Step-by-Step Solution:

1. **Identify the decay constant (λ)**:
\[ \lambda = 0.2166 \, \text{per day} \]

2. **Use the formula for average life (τ)**:
\[ \tau = \frac{1}{\lambda} \]

3. **Substitute the value of λ into the formula**:
\[ \tau = \frac{1}{0.2166} \]

4. **Calculate τ**:
\[ \tau \approx 4.617 \, \text{days} \]

5. **Final Result**:
The average life (τ) of the radioactive material is approximately:
\[ \tau \approx 4.617 \, \text{days} \]