A black body at 200 K is found to emit maximum energy at a wavelength of `14mu m`. When its temperature is raised to 1000 K, the wavelength at which maximum energy is emitted is

Options

A. `14mum`.
B. `70mum`.
C. `2.8mum`
D. `2.8mum`.

Explanation

To solve the problem, we will use Wien's Displacement Law, which states that the product of the wavelength at which maximum energy is emitted (λm) and the absolute temperature (T) of a black body is a constant.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Initial Temperature (T1) = 200 K
- Wavelength corresponding to T1 (λm1) = 14 μm
- Final Temperature (T2) = 1000 K
- Wavelength corresponding to T2 (λm2) = ?

2. **Apply Wien's Displacement Law**:
According to Wien's Displacement Law:
\[ λm \cdot T = \text{constant} \]
Therefore, we can write:
\[ λm1 \cdot T1 = λm2 \cdot T2 \]

3. **Substitute the Known Values**:
Substitute the values we have into the equation:
\[ 14 \, \mu m \cdot 200 \, K = λm2 \cdot 1000 \, K \]

4. **Rearrange the Equation to Solve for λm2**:
Rearranging gives us:
\[ λm2 = \frac{14 \, \mu m \cdot 200 \, K}{1000 \, K} \]

5. **Calculate λm2**:
Now perform the calculation:
\[ λm2 = \frac{2800 \, \mu m \cdot K}{1000 \, K} = 2.8 \, \mu m \]

6. **Final Answer**:
The wavelength at which maximum energy is emitted when the temperature is raised to 1000 K is:
\[ λm2 = 2.8 \, \mu m \]

### Summary:
The wavelength at which maximum energy is emitted when the temperature is raised to 1000 K is **2.8 μm**.