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The radiation emerging from a furnace (blackbody) is found to have a most probable wavelength \(\lambda_m\) and the gas molecules (air) emerging from it have an RMS speed \(v.\) As the temperature of the furnace is varied:
1. \(\lambda_m\propto v \) 2. \(\lambda_m\propto \dfrac1v \)
3. \(\lambda_m\propto v^2 \) 4. \(\lambda_m\propto \dfrac1{v^2} \)
Subtopic:  Wien's Displacement Law |
 65%
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When radiant energy from a blackbody at temperature \(T,\) is analysed, and the most probable wavelength of the radiation is \(\lambda_{\text{mp}},\) then:
1. \(\lambda_{\text{mp}}\propto T\)
2. \(\lambda_{\text{mp}}\propto \Large\frac1T\)
3. \(\lambda_{\text{mp}}\propto T^{1/2}\)
4. \(\lambda_{\text{mp}}\propto T^{\text-1/2}\)
Subtopic:  Wien's Displacement Law |
 79%
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Gas molecules at a temperature \(T\) are enclosed within a thin-walled enclosure, the inner and outer walls having the same temperature \(T\) in equilibrium. The rms speed of the gas molecules is \(v_{\text{rms}}.\) The enclosure radiates outward as a blackbody, and the most probable wavelength is \(\lambda_{\text{mp}},\) in the blackbody radiation. As the temperature of the gas varies, so do \(v_{\text{rms}}\) and \(\lambda_{\text{mp}}.\) The relationship between \(v_{\text{rms}}\) and \(\lambda_{\text{mp}}\) is:
1. \(\lambda_{\text{mp}}v_{\text{rms}}=\text{constant}\)    2. \(\Large\frac{\lambda_{\text{mp}}}{v_{\text{rms}}}\)\(=\text{constant}\)   
3. \(\lambda_{\text{mp}}v^2_{\text{rms}}=\text{constant}\) 4. \(\Large\frac{\lambda_{\text{mp}}}{v^2_{\text{rms}}}\)\(=\text{constant}\)
Subtopic:  Wien's Displacement Law |
 64%
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The value of Wien's constant, \(b\) is \(3\times10^{-3}~\text{m-K}.\) The cosmic background radiation can be considered to be equivalent to a blackbody radiation at \(3~\text K.\) The most probable wavelength in this radiation is:
1. \(1~\text{mm}\)
2. \(1~\text{m}\)
3. \(10^3~\text{m}\)
4. \(1~\mu\text{m}\)
Subtopic:  Wien's Displacement Law |
 80%
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The maximum intensity of emission occurs at a wavelength of \(1~\mu \text{m}\) in the spectrum of radiation emitted by a star. Take Wien's constant as \(3~\text{mm}\text-\text{K}.\) The surface temperature of the star is (nearly):
1. \(1000~\text K\) 2. \(3000~\text K\)
3. \(1000^\circ\text C\) 4. \(3000^\circ\text C\)
Subtopic:  Wien's Displacement Law |
 88%
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Radiant light from three different stars \(A,B,C\) arriving on the Earth is analysed by a prism and the intensities \((I)\) are plotted as a function of wavelength \((\lambda).\) If the absolute temperatures of the stars are \(\theta_A,\theta_B,\theta_C\) then:
1. \(\theta_B>\theta_A=\theta_C\)
2. \(\theta_A>\theta_B>\theta_C\)
3. \(\theta_C>\theta_B>\theta_A\)
4. \(\theta_B<\theta_A=\theta_C\)
Subtopic:  Wien's Displacement Law |
 68%
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Given below are two statements:
Statement I: If the absolute surface temperature of a star doubles, the most probable wavelength in the radiation spectrum also doubles.
Statement II: If the absolute surface temperature of a star doubles, the rate of radiant energy loss from the star increases to \(16\) times its initial value.
 
1. Statement I is incorrect and Statement II is correct.
2. Both Statement I and Statement II are correct.
3. Both Statement I and Statement II are incorrect.
4. Statement I is correct and Statement II is incorrect.
Subtopic:  Wien's Displacement Law |
 73%
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The radiant emission spectrum from a blackbody shows a peak at a wavelength of \(3~\mu\text m.\) The temperature of the blackbody is nearly: 
(take Wien's constant \(=3~\text{mm}\cdot\text{K}\)):
1. \(1000^\circ\text C\) 2. \(1000~\text K\)
3. \(10000~\text K\) 4. \(10^5~\text K\)
Subtopic:  Wien's Displacement Law |
 86%
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