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 of finding the wavelength corresponding to maximum intensity when the temperature of a body increases from 27°C to 327°C, we can use Wien's displacement law. Here’s a step-by-step solution:

### Step 1: Understand Wien's Displacement Law
Wien's displacement law states that the wavelength corresponding to the maximum intensity of radiation emitted by a black body is inversely proportional to its absolute temperature. Mathematically, it is expressed as:
\[ \lambda_m \cdot T = b \]
where:
- \( \lambda_m \) is the wavelength of maximum intensity,
- \( T \) is the absolute temperature in Kelvin,
- \( b \) is Wien's constant.

### Step 2: Convert Temperatures to Kelvin
We need to convert the given temperatures from Celsius to Kelvin:
- For the initial temperature \( T_1 = 27°C \):
\[ T_1 = 27 + 273 = 300 \, K \]
- For the final temperature \( T_2 = 327°C \):
\[ T_2 = 327 + 273 = 600 \, K \]

### Step 3: Apply Wien's Displacement Law
According to Wien's law, we can write:
\[ \lambda_{m1} \cdot T_1 = \lambda_{m2} \cdot T_2 \]
where:
- \( \lambda_{m1} \) is the initial wavelength corresponding to \( T_1 \) (let's denote it as \( \lambda \)),
- \( \lambda_{m2} \) is the final wavelength corresponding to \( T_2 \) (let's denote it as \( \lambda' \)).

Substituting the values we have:
\[ \lambda \cdot 300 = \lambda' \cdot 600 \]

### Step 4: Solve for the Final Wavelength
Rearranging the equation to find \( \lambda' \):
\[ \lambda' = \frac{\lambda \cdot 300}{600} \]
\[ \lambda' = \frac{\lambda}{2} \]

### Conclusion
Thus, the wavelength corresponding to maximum intensity when the temperature increases from 27°C to 327°C becomes:
\[ \lambda' = \frac{\lambda}{2} \]

### Final Result
The final wavelength is half of the initial wavelength.

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