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A red star and a white star radiate energy at the same rate which star is bigger?
(A) red
(B) white
(C) both have the same size
(D) cannot say anything,

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Last updated date: 13th Jun 2024
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Answer
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Hint: red star or white star both are stars but the primary difference is due to the temperatures. The colour of a star depends on its surface temperature and indirectly on their size.

Complete step by step answer:We are given a red star and a white star. Stars differ in colour varying from orange to white and blue. Colour is caused by the temperature of the surface of the star. Our Sun falls in the category of a yellow star.
White stars are very big, more powerful than our sun.
Red stars have higher temperatures than white stars.
Now, from Stefan-Boltzmann law, the total radiant heat power emitted from a surface is proportional to the fourth power of its absolute temperature.
\[\begin{align}
  & P\alpha {{T}^{4}} \\
 & E=A{{T}^{4}} \\
\end{align}\]
Where A is the area of the star. Now given in the question that the red star and a white star radiate energy at the same rate, if the rates are the same there would be a temperature change.
A red star would be half the temperature of the white star so it would need to have a radius 4 times the white star to emit the energy at the same rate. Hence, the red star would be bigger than the white star, and the correct option would be (A).

Note:Blue and green stars are normally giant young stars which are very active and they do not live for very long and they die young usually in a massive explosion called a SuperNova