If wavelength of maximum intensity of radiation emitted by Sun and Moon are 0.5 × 10-6 m and 10-4 m respectively, then the ratio of their temperature is

Question

If wavelength of maximum intensity of radiation emitted by Sun and Moon are 0.5 × 10-6 m and 10-4 m respectively, then the ratio of their temperature is (A) (1/10) (B) (1/50) (C) 100 (D) 200

Tardigrade Admin · Accepted Answer

λm T1= Constant [Wien's law] ⇒ λ1 T1=λ2 T2 0.5 × 10-6 × T1=10-4 × T2 (T1/T2)=200

Q. If wavelength of maximum intensity of radiation emitted by Sun and Moon are $0.5 \times 1 0^{- 6} m$ and $1 0^{- 4} m$ respectively, then the ratio of their temperature is

$\frac{1}{10}$

$\frac{1}{50}$

$100$

$200$

$λ_{m} T_{1} =$ Constant
[Wien's law]
$\Rightarrow λ_{1} T_{1} = λ_{2} T_{2}$
$0.5 \times 1 0^{- 6} \times T_{1} = 1 0^{- 4} \times T_{2}$
$\frac{T _{1}}{T _{2}} = 200$

Q. If wavelength of maximum intensity of radiation emitted by Sun and Moon are 0.5×10−6m and 10−4m respectively, then the ratio of their temperature is

101​

501​

100

200