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  4. Two stars radiate maximum energy at wavelengths 3.6× 10- 5cm and 4.8× 10- 5cm respectively. The ratio of their temperatures is

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Q. Two stars radiate maximum energy at wavelengths $3.6\times 10^{- 5}cm$ and $4.8\times 10^{- 5}cm$ respectively. The ratio of their temperatures is

NTA AbhyasNTA Abhyas 2022

Solution:

Let T and T' be the temperatures of the two stars and λmax and λmax' be their respective wavelengths of maximum emission.
Here, λmax = 3.6 × 10-5 cm and λmax' = 4.8 × 10-5 cm
$\text{Now,} \frac{\text{T}}{\text{T}^{′}} = \frac{\lambda _{\text{max}}^{′}}{\lambda _{\text{max}}} = \frac{\text{4.8} \times \text{10}^{- 5}}{\text{3.6} \times \text{10}^{- 5}} = \frac{4}{3}$