Question

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 1

`r_(A)=400r_(B)`
`P_(A)=10^(4)P_(B)`
`P_(A)=sigma(4pir_(A)^(2))T_(A)^(4)`
`P_(B)=sigma(4pir_(B)^(2))T_(B)^(4)`
`(P_(A))/(P_(B))=(400)^(2)((T_(A))/(T_(B)))^(4)=10^(4)`
`((T_(A))/(T_(B)))^(4)=(10^(4))/(400xx400)=(1)/(4xx4)=(1)/(24)`
`(T_(A))/(T_(B))=(1)/(2)` Now `lambda prop (1)/(T)`
`(lambda_(A))/(lambda_(B))=(T_(B))/(T_(A))=2`