Physics - Modern Physics Question with Solution | TestHub

From de Broglie's hypothesis, $\lambda =\frac{\mathrm{h}}{{\mathrm{p}}_{\mathrm{n}}}=\frac{\mathrm{h}}{\mathrm{mv}}$ and from Bohr's atomic model, $\mathrm{L}=\frac{\mathrm{nh}}{2\pi }$ Also, $\mathrm{L}={\mathrm{mvr}}_{\mathrm{n}}$ Due to quantization of angular momentum, we can write, $\begin{array}{rl}& \frac{\mathrm{nh}}{2\pi }={\mathrm{mvr}}_{\mathrm{n}}\\ \therefore & \mathrm{v}=\frac{\mathrm{nh}}{2\pi \mathrm{mr}}\end{array}$ putting (ii) into (i), we get, $\therefore \lambda =\frac{\mathrm{h}}{\mathrm{m}(\mathrm{nh}/2\pi \mathrm{mr})}=\frac{2\pi \mathrm{r}}{\mathrm{n}}$