Two spherical starts 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

Let A be the surface area of smaller body then,
`P_(A)=sigma.(16xx10^(4))AT_(A)^(4)rArrP_(B)=sigmaAT_(B)^(4)`
Now , `(16xx10^(4)T_(A)^(4))/(T_(B)^(A))=10^(4)rArr((T_(A))/(T_(B)))^(4)=(1)/(16)rArr(T_(A))/(T_(B))=(1)/(2)`
By Wein's law, `lambdaT="const"therefore"ratio"(lambda_(A))/(lambda_(B))=2`.