question_answer

A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is\[{{\text{U}}_{\text{1}}}\text{,}\] at wavelength 500 nm is \[{{\text{U}}_{2}}\] and that at 1000 nm is \[{{\text{U}}_{3}}.\] Wien's constant, \[\text{b = 2}\text{.88  }\!\!\times\!\!\text{  1}{{\text{0}}^{\text{6}}}\text{ nmK}\text{.}\]Which of the following is correct?                                                                                                              

A)  \[{{\text{U}}_{1}}=0\]                  

B)   \[{{\text{U}}_{3}}=0\]

C)   \[{{\text{U}}_{\text{1}}}\text{ }{{\text{U}}_{\text{2}}}\]                            

D)   \[{{\text{U}}_{2}}\text{ }{{\text{U}}_{1}}\]

Correct Answer: D

Solution :

                 Maximum amount of emitted radiation corresponding to \[{{\lambda }_{m}}=\frac{b}{T}\] \[{{\lambda }_{m}}=\frac{2.88\times {{10}^{6}}\,nmK}{5760K}=500\,nm\] From the graph \[{{\text{U}}_{\text{1}}}\text{ }{{\text{U}}_{\text{2}}}\text{ }{{\text{U}}_{\text{3}}}\]