The half life of a radio nuclide is 77 days then its decay constant is

Options

A. 0.003/day
B. 0.006/day
C. 0.009/day
D. 0.012/day

Explanation

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

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

### Step-by-Step Solution:

1. **Identify the half-life**:
The problem states that the half-life (t_half) of the radionuclide is 77 days.

2. **Write down the formula for decay constant**:
The formula relating the half-life to the decay constant is:
\[ \lambda = \frac{0.693}{t_{half}} \]

3. **Substitute the half-life value into the formula**:
Substitute \(t_{half} = 77 \text{ days}\) into the formula:
\[ \lambda = \frac{0.693}{77} \]

4. **Calculate the decay constant**:
Now, perform the calculation:
\[ \lambda = \frac{0.693}{77} \approx 0.0090 \text{ days}^{-1} \]

5. **Final Answer**:
The decay constant (λ) is approximately:
\[ \lambda \approx 0.0090 \text{ days}^{-1} \]