Question

find the velocity (m/s) of electron in first bohr’s orbit of radius a0. Also find the de brogile ‘s wavelength (in m ). Find the orbital angular momentum of 2p orbital of hydrogen atom in units of h/2pie.

Answer 1

$$\begin{gathered} 1.ForhydrogenatomZ=1:n=1 \\ Velocity=2.18\times {10}^6\times \frac{Z}{n} \\ =2.18\times {10}^6\times \frac{1}{1}=2.18\times {10}^{6}m/s \\ 2.\lambda =\frac{h}{mv} \\ =\frac{6.626\times {10}^{-34}}{9.1\times {10}^{-31}\times 2.18\times {10}^6} \\ =3.34\times {10}^{-10}m=3.34A^0 \\ 3.For2p:l=1 \\ Orbitalangularmomentum=\sqrt{l(l+1)}\times \frac{h}{2\mathrm{\pi }} \\ =\sqrt{1(1+1)}\times \frac{h}{2\mathrm{\pi }}=\sqrt{2}\times \frac{h}{2\mathrm{\pi }}=\frac{h}{\sqrt{2}\mathrm{\pi }} \end{gathered}$$