Question

The colour of a star depends upon its ____________.
A) density
B) distance from the sun
C) surface temperature
D) radius

Answer 1

Hint:The three most important properties of stars are its mass, its luminosity and its temperature. The colour of a star and its temperature are closely related to one another. Wien’s displacement law describes the relationship between the temperature of the star and its colour.

Formula used:
The relation between temperature and wavelength as obtained by Wein is given by, ${\lambda }_{max}={\displaystyle \frac{b}{T}}$ where ${\lambda }_{max}$ is the peak wavelength, $b$ is a constant and $T$ is the surface temperature of the black body.

Complete step by step answer.
Step 1: Express the Wien’s displacement law to find the dependence of the colour of a star.
Wien’s displacement law is based on the fact that the hotter an object is, the more energy it possesses and therefore will emit radiation at higher frequencies.

The colour of a star is described by the wavelength of the radiation it emits. The star can be assumed to be a black body.

Wein found that the radiation curve of the black body for different temperatures peaks at different wavelengths. Wein obtained the wavelength of the emitted radiation to be inversely proportional to the surface temperature of the body.
Wien’s law can be expressed as ${\lambda }_{max}={\displaystyle \frac{b}{T}}$ where ${\lambda }_{max}$ is the peak wavelength, $b$ is some constant and $T$ is the surface temperature of the black body.
So the colour depends on the surface temperature of the star.

Thus the correct option is C.

Additional information:

A star is a luminous ball of gas which consists mostly of hydrogen and helium and is held together by its own gravity. Stars radiate energy which is released by the thermonuclear fusion reaction occurring within it.

Note: A black body is an ideal body that absorbs all electromagnetic radiation which is incident on it, irrespective of the frequency of the incident radiation or the angle at which it is incident. Higher frequency radiation will have a shorter wavelength. So hotter objects like the outer zone of a candle flame will appear blue in colour as blue light has the shorter wavelength.