A black body emits radiation of maximum intensity at a wavelength of 5000A when the temperature of the body is `1227^(@)`C. If the temperature of the body is increased by `1000^(@)`C, calculate the wavelength corresponding to the maximum intensity.

Explanation

To solve the problem, we will use Wien's Displacement Law, which states that the wavelength corresponding to the maximum intensity of radiation emitted by a black body is inversely proportional to its temperature.

### Step-by-Step Solution:

1. **Convert Initial Temperature to Kelvin**:
- The initial temperature given is \( T_1 = 1227^\circ C \).
- To convert Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
- Therefore,
\[ T_1 = 1227 + 273 = 1500 \, K \]

2. **Calculate the New Temperature**:
- The temperature is increased by \( 1000^\circ C \).
- The new temperature \( T_2 \) is:
\[ T_2 = 1227 + 1000 = 2227^\circ C \]
- Convert this to Kelvin:
\[ T_2 = 2227 + 273 = 2500 \, K \]

3. **Use Wien's Displacement Law**:
- According to Wien's Displacement Law:
\[ \lambda_{m1} \cdot T_1 = \lambda_{m2} \cdot T_2 \]
- Rearranging gives:
\[ \lambda_{m2} = \lambda_{m1} \cdot \frac{T_1}{T_2} \]

4. **Substitute Known Values**:
- We know:
- \( \lambda_{m1} = 5000 \, \text{Å} \)
- \( T_1 = 1500 \, K \)
- \( T_2 = 2500 \, K \)
- Substitute these values into the equation:
\[ \lambda_{m2} = 5000 \cdot \frac{1500}{2500} \]

5. **Simplify the Calculation**:
- Simplifying the fraction:
\[ \frac{1500}{2500} = \frac{3}{5} \]
- Therefore:
\[ \lambda_{m2} = 5000 \cdot \frac{3}{5} = 3000 \, \text{Å} \]

### Final Answer:
The wavelength corresponding to the maximum intensity at the new temperature is \( \lambda_{m2} = 3000 \, \text{Å} \).

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