If the half life of radium is 1620 years then its decay constant is

Options

A. `4.2xx10^(-4)` per year
B. `2.4xx10^(-4)` per year
C. `4.2xx10^(-2)` per year
D. `2.4xx10^(-2)` per year

Explanation

To find the decay constant (λ) of radium given its half-life (t_half), we can use the relationship between half-life and decay constant, which is given by the formula:

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Half-life of radium (t_half) = 1620 years.

2. **Rearranging the formula**:
- We need to find the decay constant (λ). Rearranging the formula gives:
\[ \lambda = \frac{0.693}{t_{half}} \]

3. **Substituting the known value**:
- Substitute the half-life value into the equation:
\[ \lambda = \frac{0.693}{1620} \]

4. **Calculating the decay constant**:
- Perform the division:
\[ \lambda = 0.00042778 \text{ years}^{-1} \]

5. **Expressing in scientific notation**:
- To express this in scientific notation, we can write:
\[ \lambda \approx 4.27 \times 10^{-4} \text{ years}^{-1} \]

### Final Answer:
The decay constant (λ) of radium is approximately \(4.27 \times 10^{-4} \text{ years}^{-1}\).