Calculate the temperature at which a body may appear (i) deep red (7900A) and (ii) blue (5000A).

Explanation

To solve the problem of calculating the temperature at which a body may appear deep red (7900 Å) and blue (5000 Å), we will use Wien's Displacement Law. This law states that the wavelength of the peak emission of a black body is inversely proportional to its temperature. The formula can be expressed as:

\[ \lambda \cdot T = b \]

where:
- \(\lambda\) is the wavelength in meters,
- \(T\) is the temperature in Kelvin,
- \(b\) is Wien's displacement constant, approximately \(3 \times 10^{-3} \, \text{m} \cdot \text{K}\).

### Step-by-Step Solution:

#### Part (i): Deep Red (7900 Å)

1. **Convert the wavelength from Ångströms to meters:**
\[ \lambda = 7900 \, \text{Å} = 7900 \times 10^{-10} \, \text{m} = 7.9 \times 10^{-7} \, \text{m} \]

2. **Use Wien's Displacement Law to find the temperature:**
\[ T = \frac{b}{\lambda} \]
Substituting the values:
\[ T = \frac{3 \times 10^{-3} \, \text{m} \cdot \text{K}}{7.9 \times 10^{-7} \, \text{m}} \]

3. **Calculate the temperature:**
\[ T \approx \frac{3 \times 10^{-3}}{7.9 \times 10^{-7}} \approx 3.797 \times 10^{3} \, \text{K} \approx 3.8 \times 10^{3} \, \text{K} \]

#### Part (ii): Blue (5000 Å)

1. **Convert the wavelength from Ångströms to meters:**
\[ \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5.0 \times 10^{-7} \, \text{m} \]

2. **Use Wien's Displacement Law to find the temperature:**
\[ T = \frac{b}{\lambda} \]
Substituting the values:
\[ T = \frac{3 \times 10^{-3} \, \text{m} \cdot \text{K}}{5.0 \times 10^{-7} \, \text{m}} \]

3. **Calculate the temperature:**
\[ T \approx \frac{3 \times 10^{-3}}{5.0 \times 10^{-7}} \approx 6.0 \times 10^{3} \, \text{K} \]

### Final Results:
- The temperature for the body appearing deep red (7900 Å) is approximately **3800 K**.
- The temperature for the body appearing blue (5000 Å) is approximately **6000 K**.