The wavelength of maximum energy released during an atomic axplosion was `2.93xx10^(-10)m`. Given that Wien's constant is `2.93xx10^(-3)m-K`, the maximum temperature attained must be of the order of

Options

A. `10^(-7)`K
B. `10^7K`
C. `10^(-13)K`
D. `5.86xx10^7K`

Explanation

To find the maximum temperature attained during an atomic explosion given the wavelength of maximum energy released, we can use Wien's displacement law. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Wavelength of maximum energy released, \( \lambda_m = 2.93 \times 10^{-10} \, \text{m} \)
- Wien's constant, \( b = 2.93 \times 10^{-3} \, \text{m-K} \)

2. **Use Wien's Displacement Law:**
According to Wien's displacement law, the relationship between the wavelength of maximum energy and temperature is given by:
\[ \lambda_m \cdot T = b \]
where \( T \) is the temperature in Kelvin.

3. **Rearrange the Formula to Solve for Temperature:**
We can rearrange the equation to find the temperature:
\[ T = \frac{b}{\lambda_m} \]

4. **Substitute the Values:**
Substitute the known values into the equation:
\[ T = \frac{2.93 \times 10^{-3} \, \text{m-K}}{2.93 \times 10^{-10} \, \text{m}} \]

5. **Perform the Calculation:**
Simplifying the right-hand side:
\[ T = \frac{2.93}{2.93} \times \frac{10^{-3}}{10^{-10}} = 1 \times 10^{7} \, \text{K} \]
Therefore,
\[ T = 10^7 \, \text{K} \]

6. **Conclusion:**
The maximum temperature attained during the atomic explosion is of the order of \( 10^7 \, \text{K} \).