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State and explain Wien's displacement law.

Answer» <html><body><p></p>Solution :Thermal radiation <a href="https://interviewquestions.tuteehub.com/tag/emitted-7679123" style="font-weight:bold;" target="_blank" title="Click to know more about EMITTED">EMITTED</a> by a body consists of electromagnetic waves of different wavelengths and wavelengths of these waves <a href="https://interviewquestions.tuteehub.com/tag/form-996208" style="font-weight:bold;" target="_blank" title="Click to know more about FORM">FORM</a> a continuous spectrum, but amount of electromagnetic waves of certain definite frequencies is more. <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P2_C11_E01_045_S01.png" width="80%"/> <br/> 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). <br/> On increasing its temperature, the amount of waves of smaller wavelength increases. <br/> At about 1100 K, as the waves of wavelength corresponding to red colour is more, the body appears red. <br/> Figure shows the graph of spectral emissive power `W_(lamda)` versus wavelengths `(lamda_(m))` at different temperatures. <br/> From the graph it is clear that with increase in temperature, wavelength `(lamda_(m))` corresponding to the maximum value of `W_(lamda)` decreases. <br/> Wien.s displacement law : ..The wavelength `(lamda_(m))` of a emitted radiation from the surface of any body is <a href="https://interviewquestions.tuteehub.com/tag/inversely-7688775" style="font-weight:bold;" target="_blank" title="Click to know more about INVERSELY">INVERSELY</a> <a href="https://interviewquestions.tuteehub.com/tag/proportional-1170279" style="font-weight:bold;" target="_blank" title="Click to know more about PROPORTIONAL">PROPORTIONAL</a> to the <a href="https://interviewquestions.tuteehub.com/tag/absolute-11456" style="font-weight:bold;" target="_blank" title="Click to know more about ABSOLUTE">ABSOLUTE</a> temperature of the emitting surface... <br/> `:." "lamda_(m)T=` constant <br/> The above equation is called the Wien.s displacement law. <br/> The constant in above equation is called Wien.s constant and its value is `2.9xx10^(-3)" mK"` <br/> 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)]`. <br/> This rule explains that by heating iron piece why it becomes first reddish, then greenish yellow and white at last. <br/> Wien.s law is useful to estimate temperature of surface of space objects like Sun, Moon and Star. <br/> Intensity of light is maximum for `14mum` wavelength from Moon and temperature of Moon is approximated as 200 K is as below, <br/> Here, `lamda_(m)=14mum=14xx10^(-6)m` <br/> Now from Wien.s law, <br/> `lamda_(m)T=` constant <br/> `:." T = "("constant")/(lamda_(m))=(2.9xx10^(-3))/(14xx10^(-6))` <br/> `T=207K` <br/> `:.T~~200K` <br/> Intensity of light is maximum for `lamda_(m)=4753Å` wavelength from Sun. Hence,according to Wien.s law, <br/> `lamda_(m)" T = constant"` <br/> `:.T=("constant")/(lamda_(m))` <br/> `:.T=(2.9xx10^(-3))/(4753xx10^(-10))` <br/> `=0.00061014xx10^(7)` <br/> `~~6101K` <br/> `~~6060` K (Value of textbook) <br/> This is temperature of surface of Sun not of inner side. <br/> The meaningful of surface of Sun not of inner side. <br/> 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.</body></html>


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