Question

The surface temperature of the sun which has maximum energy emission at 500 nm is 6000K. The temperature of a star which has maximum energy emission at 400 nm will be:
A. 8500K
B. 4500K
C. 7500K
D. 6500K

Answer 1

Hint: The concept to be used is wien's displacement law. Apply the wien's displacement law at the maximum intensity and substitute the given values of the wavelength and the temperature to the value of the unknown temperature of the star.

Step by step solution:
We know that the wien's displacement law is given as at maximum intensity as :
The product of the wavelength and temperature is constant.
We get that $\lambda_1 T_1 = \lambda_2 T_2 $
Where the $\lambda $ is equal to the wavelength of the radiation
The temperature is denoted by the T
Now we are given that the value of maximum energy emission occurs at 500nm
So we get $\lambda _1 = 500nm$
We are given the value of the maximum energy emission occurs at a wavelength of 400 nm for the star
We get for the star as $\lambda_2 = 400 nm$
So we now are given the value of the temperature of the sun as $T_1$ = 6000K
Here the K denotes the Kelvin scale
Now let us assume that the temperature of the star as $T_2$
So we now get the value of the Temperature of the star as :
$\lambda_1 T_1 = \lambda_2 T_2 $
500nm $ \times $ 6000 = 400nm $ \times $ $T_2$
So we get the unknown value as $T_2 = \dfrac{500 \times 6000}{400} $
$T_2 = 7500 K $
So using the wien's displacement law we found the value of the temperature of the star as 7500K

Note: We have used the Wien's displacement law in this case for the condition that the given wavelength is at the maximum intensity of the emission and we cannot use the same equation if the intensity given is not maximum and we need to take care of this condition while solving the problem of this type.