Question

An electron changes its position from orbitn = 2 to the orbit n = 4 of an atom. The wavelength of the emitted radiations is (R = R vdbergs constant)

• A. $ \mu $
• B. $ \frac{1}{2}m{{v}^{2}}=\mu mgs $
• C. $ \frac{1}{2}m{{v}^{2}}=\frac{1}{2}\times 10\times {{(10)}^{2}}=500kg.m/s. $
• D. $ v=10m/s,\mu =0.5,\,m=10kg,\,g=10m/{{s}^{2}} $

Answer 1

Answer: (B)

Wavelength of lines emitted is $ \frac{1}{\lambda }=R\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right) $ where R Rydbergs 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}{3R} $