question_answer

An electron changes its position from orbit \[n=2\] to the orbit \[n=4\] of an atom. The wavelength of the emitted radiations is:                                                                                                                                      [BHU PMT-2004]

A)  \[\frac{16}{R}\]                                               

B)  \[\frac{16}{3R}\]

C)  \[\frac{16}{5R}\]                                             

D)  \[\frac{16}{7R}\]

Correct Answer: B

Solution :

                 Wavelength of lines emitted is \[\frac{1}{\lambda }\] \[\frac{1}{\lambda }=R\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)\] Where \[R\] Rydberg?s constant. Given,   \[{{n}_{1}}=2,\,{{n}_{\,2}}=4\] \[\therefore \]  \[\frac{1}{\lambda }=R\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{4}^{2}}} \right)=\frac{3R}{16}\] \[\Rightarrow \]               \[\lambda =\frac{16}{3\,R}\]