Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits `10^4` times the power emitted from B. The ratio `((lambda_A)/(lambda_B))` of their wavelengths `lambda_A and lambda_B` at which the peaks occur in their respective radiation curves is

Options

A. the ratio of temperature of A and B is 2:1
B. the ratio of temperature of A and B is 1:2
C. the ratio of wavelength of A and B is 2:1
D. the ratio of temperature of A and B is 1:2

Answer

B, C

Explanation

Ratio of energy radiated per unit time is
`(E_A)/(E_B) = (sigma T_A^4 A_A)/(sigma T_B^4 A_B)`
` rArr 10^4 = (sigma T_A^4 xx 4pi (400 r_B)^2)/(sigma T_B^4 xx 4pi r_B^2 )`
` rArr (T_B/T_A)^4 = ((400)^2)/(10^4) = 2^4`
` rArr T_B/T_A = 2:1`
From wien.s displacement law
`(lamda_B)/(lamda_A) = T_A/T_B = 1/2`
`lamda_A/lamda_B = 2:1`