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Question: The temperature of the sun is \(5500K\)and it emits maximum intensity radiation in the yellow region...

The temperature of the sun is 5500K5500Kand it emits maximum intensity radiation in the yellow region (5.5×10−7m)\left( {5.5 \times {{10}^{ - 7}}m} \right). The maximum radiation from the furnace occurs at wavelength 11×10−7m11 \times {10^{ - 7}}m. The temperature of the furnace is
A. 1125K1125K
B. 2750K2750K
C. 5500K5500K
D. 11000K11000K

Explanation

Solution

In this question, we are given the maximum intensity wavelength of the sun and its temperature. We have found the temperature of the furnace whose wavelength is given. So, for such questions we can use the Wien displacement law. Whose expression is λmT=const{\lambda _m}T = const where λm{\lambda _m} is the wavelength and TT is the temperature.

Complete step by step answer:
According to the Wein displacement law, it states that the black body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature.
λm∝1T{\lambda _m} \propto \dfrac{1}{T} where λm{\lambda _m} is the maximum wavelength and TT is the temperature of the radiation.
Or λmT=b(const){\lambda _m}T = b(const)
According to the question:
Temperature of the sun is T1{T_1} =5500K = 5500Kand wavelength be given by λ1=5.5×10−7m{\lambda _1} = 5.5 \times {10^{ - 7}}m
And the wavelength of the furnace can be given by λ2=11×10−7{\lambda _2} = 11 \times {10^{ - 7}} and temperature of the furnace=?
Using the Wien displacement law,
λ1T1=λ2T2{\lambda _1}{T_1} = {\lambda _2}{T_2}
Putting the values
5.5×10−7×5500=11×10−7×T25.5 \times {10^{ - 7}} \times 5500 = 11 \times {10^{ - 7}} \times {T_2}
∴T2=2750K\therefore{T_2} = 2750K
So, Temperature of the furnace is 2750K2750K

Hence, the correct option is B.

Note: Wien’s Law, named after the German Physicist Wilhelm Wien, tells us that objects of different temperatures emit spectra that peak at different wavelengths. Hotter objects emit radiations of shorter wavelength and hence they appear blue. Similarly, cooler objects emit radiations of longer wavelength and hence they appear reddish.Wien displacement law has nothing as displacement as its name. The term maximum wavelength is used for the wavelength with maximum energy. The value of constant for Wien displacement law is b=2.89×10−3mKb = 2.89 \times {10^{ - 3}}mK