Question

Calculate the velocity of moving electron in the third orbit of bohr's atomic model of hydrogen. Also calculate the number of revolution per second that the electron make around the nucleus.

Answer 1

Dear Student,

The computation are expressed below,

$$\begin{gathered} v_n=\frac{2.188\times {10}^{6}Z}{n} \\ forthirdorbitn=3,Z=1 \\ {v}_3=\frac{2.188\times {10}^6\times 1}{3}=7.29\times {10}^5\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right. \\ revolutionforn=3is, \\ r=2\mathrm{\pi }\times \frac{0.592\times {\mathrm{n}}^2}{\mathrm{Z}}\times {10}^{-10}=2\mathrm{\pi }\times \frac{0.592\times 3^2}{1}\times {10}^{-10}=3.35\times {10}^{-9}\mathrm{m} \\ \mathrm{Time}=\frac{3.35\times {10}^{-9}}{3.27\times {10}^6}=1.02\times {10}^{-15} \\ \mathrm{No}.\mathrm{of}\mathrm{revolution}=\frac{1}{\mathrm{T}}=\frac{1}{1.02\times {10}^{-15}}=9.76\times {10}^{14} \end{gathered}$$

Regards.