The decay constant of a radioactive element is `3 xx 10^(-6) "min"^(-1)`. Its half-life is

Options

A. `2.31 xx 10^(5)` min
B. `2.31 xx 10^(6)` min
C. `2.31 xx 10^(-6)` min
D. `2.31 xx 10^(-7)` min

Explanation

To find the half-life of a radioactive element given its decay constant, we can use the formula:

\[ t_{1/2} = \frac{0.693}{\lambda} \]

where:
- \( t_{1/2} \) is the half-life,
- \( \lambda \) is the decay constant.

### Step-by-Step Solution:

1. **Identify the decay constant**:
The decay constant \( \lambda \) is given as \( 3 \times 10^{-6} \, \text{min}^{-1} \).

2. **Substitute the decay constant into the half-life formula**:
\[ t_{1/2} = \frac{0.693}{3 \times 10^{-6}} \]

3. **Calculate the denominator**:
The denominator is \( 3 \times 10^{-6} \).

4. **Perform the division**:
\[ t_{1/2} = \frac{0.693}{3 \times 10^{-6}} = \frac{0.693}{3} \times 10^{6} \]

5. **Calculate \( \frac{0.693}{3} \)**:
\[ \frac{0.693}{3} = 0.231 \]

6. **Combine the results**:
\[ t_{1/2} = 0.231 \times 10^{6} = 2.31 \times 10^{5} \, \text{minutes} \]

### Final Answer:
The half-life of the radioactive element is \( 2.31 \times 10^{5} \, \text{minutes} \).

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