If the temperature of the body is increases from 27°C to 327°C then wavelength corresponding to maximum intensity becomes

Options

A. Double
B. Remain same
C. Half
D. Thole

Answer

To solve the problem, we will use Wien's Displacement Law, which states that the product of the wavelength at which the intensity is maximum (λ_max) and the absolute temperature (T) is a constant. The formula is given by:

\[ \lambda_{\text{max}} \cdot T = b \]

where \( b \) is Wien's displacement constant.

### Step-by-Step Solution:

1. **Convert the temperatures from Celsius to Kelvin**:
- The initial temperature \( T_1 \) is 27°C.
- To convert to Kelvin:
\[ T_1 = 27 + 273 = 300 \, \text{K} \]
- The final temperature \( T_2 \) is 327°C.
- To convert to Kelvin:
\[ T_2 = 327 + 273 = 600 \, \text{K} \]

2. **Apply Wien's Displacement Law**:
- According to Wien's law:
\[ \lambda_1 \cdot T_1 = \lambda_2 \cdot T_2 \]
- Here, \( \lambda_1 \) is the initial wavelength and \( \lambda_2 \) is the new wavelength.

3. **Substitute the known values**:
- We can write:
\[ \lambda_1 \cdot 300 = \lambda_2 \cdot 600 \]

4. **Rearranging the equation**:
- To find \( \lambda_2 \):
\[ \lambda_2 = \frac{\lambda_1 \cdot 300}{600} \]
- Simplifying this gives:
\[ \lambda_2 = \frac{\lambda_1}{2} \]

5. **Conclusion**:
- The new wavelength \( \lambda_2 \) is half of the initial wavelength \( \lambda_1 \):
\[ \lambda_2 = \frac{\lambda_1}{2} \]

### Final Answer:
The wavelength corresponding to maximum intensity becomes half of the original wavelength.

---