Question

Our Sun emits most of its radiation at a wavelength of 550 nm. If a star were 3.50 times hotter than our Sun, it would emit most of its radiation at a wavelength of _______ nm

Answer 1

The wavelength of the radiation emitted by the star is 183 nm.

Explanation:

As per Wien's displacement law, the product of emitted wavelength and temperature of the star will be equal to 2.898 × 10⁻³ mK.

$T*wavelength = 2.898 * 10^{-3}$

So if the wavelength of the emitted radiation by Sun is given as 550 nm, then the temperature of the Sun will be

$Temperature of Sun = \frac{2.898*10^{-3} }{wavelength}$

$Temperature of Sun = \frac{2.898*10^{-3} }{550 * 10^{-9} } = 5.27 * 10^{3} K$

Then if the temperature of star is said to be 3.5 times hotter than Sun, then the temperature of Star = 3.5×5.27×10³ = 15.81×10³ K.

With this temperature, the wavelength of the emitted radiation can be found as follows:

$Wavelength = \frac{2.898 * 10^{-3} }{15.81 * 10^{3} } =183 nm$

So, the wavelength of the radiation emitted by the star is 183 nm.