On observing light from three different stars $P$, $Q$, and $R$, it was found that the intensity of the violet

Question

On observing light from three different stars $P$, $Q$, and $R$, it was found that the intensity of the violet colour is maximum in the spectrum of $P$, the intensity of the green colour is maximum in the spectrum of $R$ and the intensity of the red colour is maximum in the spectrum of $Q$. If $T_P$, $T_Q$, and $T_R$ are the respective absolute temperatures of $P$, $Q$, and $R$, then it can be concluded from the above observations that:

Accepted Answer

According to Wien's displacement law, the wavelength corresponding to maximum spectral emissive power is inversely proportional to the absolute temperature of the emitting body ($\lambda_{ ext{max}} \propto \frac{1}{T}$). The order of wavelengths for the given colours in the visible spectrum is $\lambda_{ ext{violet}} < \lambda_{ ext{green}} < \lambda_{ ext{red}}$. Given that stars $P$, $R$, and $Q$ have maximum intensity at violet, green, and red colours respectively, we have $\lambda_P < \lambda_R < \lambda_Q$. Since temperature is inversely proportional to the wavelength of maximum intensity, the temperatures of the stars will follow the reverse order: $T_P > T_R > T_Q$.

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