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State and explain Wien's displacement law. |
Answer» Solution :Thermal radiation EMITTED by a body consists of electromagnetic waves of different wavelengths and wavelengths of these waves FORM a continuous spectrum, but amount of electromagnetic waves of certain definite frequencies is more.  For example, in black radiation at room temperature (300 K) majority of the radiation consists of electromagnetic waves of wavelength `95,500" A"^(@)` (called infrared waves). On increasing its temperature, the amount of waves of smaller wavelength increases. At about 1100 K, as the waves of wavelength corresponding to red colour is more, the body appears red. Figure shows the graph of spectral emissive power `W_(lamda)` versus wavelengths `(lamda_(m))` at different temperatures. From the graph it is clear that with increase in temperature, wavelength `(lamda_(m))` corresponding to the maximum value of `W_(lamda)` decreases. Wien.s displacement law : ..The wavelength `(lamda_(m))` of a emitted radiation from the surface of any body is INVERSELY PROPORTIONAL to the ABSOLUTE temperature of the emitting surface... `:." "lamda_(m)T=` constant The above equation is called the Wien.s displacement law. The constant in above equation is called Wien.s constant and its value is `2.9xx10^(-3)" mK"` Remember : Here `lamda_(m)` is not maximum wavelength but radiation energy is maximum Value of Wien.s constant is `2.9xx10^(-3)" mK"` and 0.290 cm K in CGS system and dimensional formula is `[M^(0)L^(1)T^(0)K^(1)]`. This rule explains that by heating iron piece why it becomes first reddish, then greenish yellow and white at last. Wien.s law is useful to estimate temperature of surface of space objects like Sun, Moon and Star. Intensity of light is maximum for `14mum` wavelength from Moon and temperature of Moon is approximated as 200 K is as below, Here, `lamda_(m)=14mum=14xx10^(-6)m` Now from Wien.s law, `lamda_(m)T=` constant `:." T = "("constant")/(lamda_(m))=(2.9xx10^(-3))/(14xx10^(-6))` `T=207K` `:.T~~200K` Intensity of light is maximum for `lamda_(m)=4753Å` wavelength from Sun. Hence,according to Wien.s law, `lamda_(m)" T = constant"` `:.T=("constant")/(lamda_(m))` `:.T=(2.9xx10^(-3))/(4753xx10^(-10))` `=0.00061014xx10^(7)` `~~6101K` `~~6060` K (Value of textbook) This is temperature of surface of Sun not of inner side. The meaningful of surface of Sun not of inner side. The meaningful characteristic of curves of radiation from black body is they at universal and only depends on temperature but not on dimension, shape or matter. |
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