A certain radioactive substance has a half-life period of 30 days. What is the disintegration constant ?

Options

A. 0.02310 per day
B. .0.02310 per month
C. 1.0231 per day
D. 2.031 per day

Answer

To find the disintegration constant (λ) of a radioactive substance given its half-life (T), we can use the following relationship:

1. **Identify the formula**: The disintegration constant (λ) is related to the half-life (T) by the formula:
\[ \lambda = \frac{\ln 2}{T} \]
where \(\ln 2\) is approximately 0.693.

2. **Substitute the half-life value**: We are given that the half-life (T) is 30 days. We can substitute this value into the formula:
\[ \lambda = \frac{0.693}{30} \]

3. **Calculate the disintegration constant**: Now, perform the division:
\[ \lambda = \frac{0.693}{30} \approx 0.0231 \text{ days}^{-1} \]

4. **State the final answer**: The disintegration constant (λ) for the radioactive substance is approximately:
\[ \lambda \approx 0.0231 \text{ days}^{-1} \]

### Summary of Steps:
1. Identify the formula relating disintegration constant and half-life.
2. Substitute the given half-life into the formula.
3. Perform the calculation to find the disintegration constant.
4. State the final answer.