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

2

Explanation

`P=e sigma AT^(-4)`
`lambdaT=` constant
`P_(A)/P_(B)=(e sigma A_(A) T_(A)^(4))/(e sigma A_(B)T_(B)^(4))=(A_(A) T_(A)^(4))/(A_(B) T_(B)^(4))=r_(A)^(2)/r_(B)^(2). lambda_(B)^(2)/lambda_(A)^(4)`
`10^(4)=400^(2).(lambda_(B)/lambda_(A))^(4)`
`10^(4)/(16xx10^(4))=(lambda_(B)/lambda_(A))^(4)`
`lambda_(A)/lambda_(B)=(16/1)^(1/4)=2`