Question
The wavelength corresponding to maximum intensity of radiation emitted by a source at temperature $$2000\,K$$ is $$\lambda ,$$ then what is the wavelength corresponding to maximum intensity of radiation at temperature $$3000\,K$$ ?
A.
$$\frac{2}{3}\lambda $$
B.
$$\frac{{16}}{{81}}\lambda $$
C.
$$\frac{{81}}{{16}}\lambda $$
D.
$$\frac{4}{3}\lambda $$
Answer :
$$\frac{2}{3}\lambda $$
Solution :
Wien’s displacement law is given by
$${\lambda _m}T = $$ constant
$${\lambda _m} = $$ Maximum wavelength radiation
$$T =$$ temperature of the body
So for two different cases, i.e. at two different temperatures
or $${\lambda _1}{T_1} = {\lambda _2}{T_2}$$
$${\lambda _2} = {\lambda _1}\left( {\frac{{{T_1}}}{{{T_2}}}} \right)$$
Given, $${T_1} = 2000\,K,{T_2} = 3000\,K,{\lambda _1} = \lambda $$
$$\therefore {\lambda _2} = \lambda \times \frac{{2000}}{{3000}} = \frac{2}{3}\lambda $$