To solve the problem, we need to analyze the power radiated by the three discs A, B, and C, taking into account their radii and the wavelengths corresponding to maximum intensity.
### Step-by-Step Solution:
1. **Understanding the Power Radiated**:
The power radiated by a black body is given by the Stefan-Boltzmann Law, which states that the power \( Q \) radiated is proportional to the area \( A \) and the fourth power of the temperature \( T \):
\[
Q \propto A T^4
\]
2. **Area Calculation**:
The area \( A \) of a disc is given by the formula:
\[
A = \pi r^2
\]
where \( r \) is the radius of the disc. For discs A, B, and C, we have:
- For disc A (radius \( r_A = 2 \, m \)):
\[
A_A = \pi (2^2) = 4\pi \, m^2
\]
- For disc B (radius \( r_B = 4 \, m \)):
\[
A_B = \pi (4^2) = 16\pi \, m^2
\]
- For disc C (radius \( r_C = 6 \, m \)):
\[
A_C = \pi (6^2) = 36\pi \, m^2
\]
3. **Wavelength and Temperature Relationship**:
According to Wien's Displacement Law, the wavelength corresponding to maximum intensity (\( \lambda_{max} \)) and temperature (\( T \)) are related as follows:
\[
\lambda_{max} T = b
\]
where \( b \) is a constant. Thus, we can express the temperature in terms of the wavelength:
\[
T = \frac{b}{\lambda_{max}}
\]
4. **Calculating the Temperatures**:
For the discs A, B, and C, we can denote their maximum wavelengths as \( \lambda_A = 300 \, nm \), \( \lambda_B = 400 \, nm \), and \( \lambda_C = 500 \, nm \). Therefore, their respective temperatures will be:
- For disc A:
\[
T_A = \frac{b}{300}
\]
- For disc B:
\[
T_B = \frac{b}{400}
\]
- For disc C:
\[
T_C = \frac{b}{500}
\]
5. **Power Ratio Calculation**:
Now we can express the power radiated by each disc in terms of their areas and temperatures:
\[
Q_A \propto A_A T_A^4 = 4\pi \left(\frac{b}{300}\right)^4
\]
\[
Q_B \propto A_B T_B^4 = 16\pi \left(\frac{b}{400}\right)^4
\]
\[
Q_C \propto A_C T_C^4 = 36\pi \left(\frac{b}{500}\right)^4
\]
6. **Simplifying the Ratios**:
We can now find the ratios \( Q_A : Q_B : Q_C \):
\[
Q_A : Q_B : Q_C = \frac{4\pi \left(\frac{b}{300}\right)^4}{16\pi \left(\frac{b}{400}\right)^4} : \frac{16\pi \left(\frac{b}{400}\right)^4}{36\pi \left(\frac{b}{500}\right)^4}
\]
Simplifying this gives:
\[
Q_A : Q_B : Q_C = \frac{4}{16} \cdot \frac{400^4}{300^4} : 1 : \frac{36 \cdot 500^4}{16 \cdot 400^4}
\]
7. **Final Comparison**:
After calculating the ratios, we find that \( Q_B \) is the maximum among the three. Thus, the answer is:
\[
\text{(b) } Q_B \text{ is maximum.}
\]
