Chemistry - Atomic Structure Question with Solution | TestHub

According to Bohr, $$\begin{array}{rl}& \mathrm{mvr}=\frac{\mathrm{nh}}{2\pi }\\ & 2\pi \mathrm{r}=\frac{\mathrm{nh}}{\mathrm{mv}}=\mathrm{n}\lambda \end{array}$$ ..(i) $\left[\because \lambda =\frac{\mathrm{h}}{\mathrm{mv}}\right]$ where, $\mathrm{r}=$ radius, $\lambda =$ wavelength $\mathrm{n}=$ number of orbit Also, $$r=\frac{a_0{n}^2}{\mathrm{Z}}$$ where, ${\mathrm{a}}_0=$ Bohr radius $=52.9\mathrm{pm}$ $\mathrm{Z}=$ atomic number On substituting the value of ' $r$ ' from Eq. (ii) to Eq. (i), we get $$\begin{array}{rl}\mathrm{n}\lambda & =\frac{2\pi {\mathrm{n}}^2{\mathrm{a}}_0}{\mathrm{Z}}\Rightarrow \lambda =\frac{2\pi {\mathrm{na}}_0}{\mathrm{Z}}\\ \lambda & =2\pi \times 2\times 52.9[\because \mathrm{n}=2,\mathrm{Z}=1]\\ & =211.6\pi \mathrm{pm}\end{array}$$