The intensity of radiation emitted by the sun has its maximum value at a wavelength of 510 nm and that emitted by the north star has the maximum value at wavelength of 350 nm . If these stars behave like black bodies, then the ratio of surface temperatures of the sun and north star is

Question

The intensity of radiation emitted by the sun has its maximum value at a wavelength of 510 nm and that emitted by the north star has the maximum value at wavelength of 350 nm . If these stars behave like black bodies, then the ratio of surface temperatures of the sun and north star is (A) 1.46 (B) 0.69 (C) 1.21 (D) 0.83

Tardigrade Admin · Accepted Answer

From Wien's displacement law λ mT =constant ⇒ λ m 1T1=λ m 2T2 Or (T1/T2)=(λ m 2/λ m 1) ...(i) Here, λ m 1=510 nm, λ m 2=350 nm So, on putting these values in Eq. (i) (T1/T2)=(350/510) ⇒ (T1/T2)=(35/51)=0.69

Q. The intensity of radiation emitted by the sun has its maximum value at a wavelength of 510nm and that emitted by the north star has the maximum value at wavelength of 350nm . If these stars behave like black bodies, then the ratio of surface temperatures of the sun and north star is

1.46

0.69

1.21

0.83

From Wien's displacement law λm​T =constant ⇒λm1​T1​=λm2​T2​ Or T2​T1​​=λm1​λm2​​ ...(i) Here, λm1​=510nm,λm2​=350nm So, on putting these values in Eq. (i) T2​T1​​=510350​⇒T2​T1​​=5135​=0.69

Q. The intensity of radiation emitted by the sun has its maximum value at a wavelength of $510 nm$ and that emitted by the north star has the maximum value at wavelength of $350 nm$ . If these stars behave like black bodies, then the ratio of surface temperatures of the sun and north star is