question_answer

The black body spectrum of an object \[250\mu F\] is such that its radiant intensity (i.e. intensity per unit wavelength interval) is maximum at a wavelength of 200 nm. Another object \[20\Omega \] has the maximum radiant intensity at 600 nm. The ratio of power emitted per unit area by source  \[9\times {{10}^{4}}\,\,Hz\]to that of source \[16\times {{10}^{7}}\,\,Hz\] is

A) \[1:81\]               

B) \[1:9\]

C) \[9:1\]                                  

D) \[81:1\]

Correct Answer: D

Solution :

From Wein's displacement law. \[\text{K},{{\text{H}}_{\text{2}}},\text{ KOH}.\text{A}l\]  \[\text{Na},{{\text{H}}_{\text{2}}},\text{ NaOH},\text{Zn}\]        \[\text{Ca}{{\text{C}}_{\text{2}}},{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{2}}},\text{Ca}{{\left( \text{OH} \right)}_{\text{2}}},\text{ Fe}\]            ??.. (i) From Boltzmann's law                                 \[Ca,{{H}_{2}},Ca{{(OH)}_{2}},Sn\] \[{{V}_{c}}\]       \[\frac{{{E}_{1}}}{{{E}_{2}}}={{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}={{\left( \frac{{{\lambda }_{{{m}_{2}}}}}{{{\lambda }_{{{m}_{1}}}}} \right)}^{4}}\]            [By Eq.(i)] \[\frac{{{V}_{c}}}{{{V}_{s}}}\approx {{10}^{-3}}\]              \[\frac{{{V}_{c}}}{{{V}_{s}}}\approx {{10}^{3}}\]