The temperature (approx) of the body omitting wavelength `0.3 mum` corresponding to maximum intensity is

Options

A. `2xx10^(4)K`
B. `10^(4)K`
C. `2 xx 10^(3)K`
D. `10^(3)K`

Explanation

To solve the problem of finding the temperature of a body emitting radiation at a wavelength of \(0.3 \, \mu m\) (micrometers) corresponding to maximum intensity, we can use Wien's Displacement Law. Here are the steps to arrive at the solution:

### Step-by-Step Solution:

1. **Understand Wien's Displacement Law**:
Wien's Displacement Law states that the wavelength at which the intensity of radiation is maximum (\(\lambda_{max}\)) is inversely proportional to the absolute temperature (T) of the black body. The formula is given by:
\[ \lambda_{max} \cdot T = b \]
where \(b\) is Wien's displacement constant, approximately equal to \(2.9 \times 10^{-3} \, \text{m} \cdot \text{K}\).

2. **Convert Wavelength to Meters**:
The given wavelength is \(0.3 \, \mu m\). We need to convert this to meters:
\[ \lambda_{max} = 0.3 \, \mu m = 0.3 \times 10^{-6} \, m = 3.0 \times 10^{-7} \, m \]

3. **Rearrange the Formula to Find Temperature**:
We can rearrange the formula to solve for temperature (T):
\[ T = \frac{b}{\lambda_{max}} \]

4. **Substitute the Values**:
Now we substitute the values of \(b\) and \(\lambda_{max}\) into the equation:
\[ T = \frac{2.9 \times 10^{-3} \, \text{m} \cdot \text{K}}{0.3 \times 10^{-6} \, \text{m}} \]

5. **Calculate the Temperature**:
Performing the calculation:
\[ T = \frac{2.9 \times 10^{-3}}{0.3 \times 10^{-6}} = \frac{2.9}{0.3} \times 10^{3} = 9.67 \times 10^{3} \, \text{K} \approx 9700 \, \text{K} \]

6. **Final Approximation**:
Since we are asked for an approximate value, we can round this to:
\[ T \approx 10^{4} \, \text{K} \]

### Conclusion:
The approximate temperature of the body emitting radiation at a wavelength of \(0.3 \, \mu m\) corresponding to maximum intensity is \(10^{4} \, \text{K}\).