If half life of radioactive atom is 2.3 days, then its decay constant would be :

Options

A. `0.1 "days"^(-1)`
B. `0.2 "days"^(-1)`
C. `0.3 "days"^(-1)`
D. `2.3 "days"^(-1)`

Answer

To find the decay constant (λ) of a radioactive atom given its half-life (t_half), we can use the following formula:

\[ \lambda = \frac{0.693}{t_{half}} \]

### Step-by-Step Solution:

1. **Identify the Half-Life**:
- We are given that the half-life (t_half) of the radioactive atom is 2.3 days.

2. **Use the Decay Constant Formula**:
- The formula for the decay constant (λ) is:
\[ \lambda = \frac{0.693}{t_{half}} \]

3. **Substitute the Half-Life into the Formula**:
- Substitute t_half = 2.3 days into the formula:
\[ \lambda = \frac{0.693}{2.3} \]

4. **Calculate the Decay Constant**:
- Perform the division:
\[ \lambda \approx 0.3 \text{ days}^{-1} \]

5. **Select the Correct Option**:
- From the options provided, the decay constant is approximately 0.3 days^{-1}, which corresponds to option 3.

### Final Answer:
The decay constant (λ) is approximately **0.3 days^{-1}**.

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