• # question_answer The electron in a H-atom makes transition${{n}_{1}}\to {{n}_{2}}$where, ${{n}_{1}}$and${{n}_{2}}$are principal quantum numbers of two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times the final state. Then, the possible value of${{n}_{1}}$and${{n}_{2}}$are A)  ${{n}_{1}}=4;{{n}_{2}}=1$         B)  ${{n}_{1}}=8,{{n}_{2}}=2$ C)  ${{n}_{1}}=6,{{n}_{2}}=2$                         D)  ${{n}_{1}}=4,{{n}_{2}}=2$

Time period$=\frac{\text{circumference}}{\text{velocity}}=\frac{2\pi r}{v}$ $\therefore$$T\propto r/v$ Now, radius i.e., $r\propto \frac{{{n}^{2}}}{Z}$and velocity i.e., $v\propto \frac{Z}{n}$ $\therefore$$T\propto \frac{{{n}^{3}}}{{{z}^{2}}}$for$Z=1,T\propto {{n}^{3}}$ For given case${{T}_{1}}=8{{T}_{2}}$ $\therefore$${{n}_{1}}=2{{n}_{2}}$ So, option [d] satisfies the given condition.