Question

Three discs, A, B and C having radii 2 m, 4 m and 6 m respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are 300 nm, 400 nm and 500 nm, respectively. The power radiated by them are Q_A, Q_B and Q_C respectively –

• A. Q_A is maximum
• B. Q_B is maximum
• C. Q_C is maximum
• D. Q_A = Q_B = Q_C

Answer 1

Answer: (B)

Q_B is maximum

Answer 2

Q µ AT⁴ and l_m T = constant. Hence,

Q µ$\frac{A}{(\lambda_{m})^{4}}$ or Q µ $\frac{r^{2}}{(\lambda_{m})^{4}}$

Q_A : Q_B : Q_C =$\frac{(2)^{2}}{(3)^{4}}$:$\frac{(4)^{2}}{(4)^{4}}$:$\frac{(6)^{2}}{(5)^{4}}$

=$\frac{4}{81}$:$\frac{1}{16}$:$\frac{36}{625}$

= 0.05 : 0.0625 : 0.0576

i.e., Q_B is maximum.