A black body at `1227^(@)C` emits radiations with maximum intensity at a wavelength of `5000 Å`. If the temperature of the body is increased by `1000^(@)`, the maximum intensity will be observed at

Options

A. `4000 Å`
B. `5000 Å`
C. `6000 Å`
D. `3000 Å`

Explanation

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 (λm) and the absolute temperature (T) of a black body is a constant. This can be expressed mathematically as:

\[ \lambda_m \cdot T = b \]

where \(b\) is a constant.

### Step-by-Step Solution:

1. **Convert the initial temperature from Celsius to Kelvin:**
\[ T_1 = 1227^\circ C + 273 = 1500 \, K \]

2. **Determine the initial maximum wavelength:**
\[ \lambda_{m1} = 5000 \, \text{Å} \]

3. **Calculate the new temperature after increasing by 1000°C:**
\[ T_2 = 1227^\circ C + 1000^\circ C + 273 = 2500 \, K \]

4. **Using Wien's Displacement Law, set up the equation:**
\[ \lambda_{m1} \cdot T_1 = \lambda_{m2} \cdot T_2 \]

5. **Substituting the known values into the equation:**
\[ 5000 \, \text{Å} \cdot 1500 \, K = \lambda_{m2} \cdot 2500 \, K \]

6. **Rearranging to solve for \(\lambda_{m2}\):**
\[ \lambda_{m2} = \frac{5000 \, \text{Å} \cdot 1500 \, K}{2500 \, K} \]

7. **Calculating \(\lambda_{m2}\):**
\[ \lambda_{m2} = \frac{5000 \cdot 1500}{2500} = 3000 \, \text{Å} \]

Thus, the maximum intensity will be observed at a wavelength of **3000 Å**.