Two spherical stars A and B emit black body 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 oc cur in their respective radiation curves is :

Answer

B

Explanation

Accoridng to Wien's displacement law
`lambda_(m_(A)) T_(A) = lambda_(m_(B)) T_(B)`
Ratio of energy radiated per unit time
`(E_(A))/(E_(B)) = (sigmaT_(A)^(4)A_(A))/(sigmaT_(B)^(4)A_(B))`
`(10^(4)E)/(E) = ((sigma)(4pi)(400r)^(2)T_(A)^(4))/((sigma)(4pi)(r^(2))T_(B)^(4))C`
`{(lambda_(B))/(lambda_(A))}^(4) (400)^(2) = 10^(4)`
`rArr {(lambda_(A))/(lambda_(B))}^(4) = 2^(4) rArr (lambda_(A))/(lambda_(B)) = 2`