Question

Find the velocity $\left(m{s}^{-1}\right)$ of electron in first Bohr orbit of radius $a_0$. Also find the de Broglie wavelength (in '$m$'). Find the orbital angular momentum of $2p$ orbital of hydrogen atom in units of $h/2\pi$.

Answer 1

$v=\frac{2.188\times {10}^6}{n}$ $m$ ${sec}^{-1}$
$v=\frac{2.188\times {10}^6}{1}=2.188\times {10}^6$ $m$ ${sec}^{-1}$
$\lambda =\frac{h}{mv}=\frac{6.626\times {10}^{-34}}{9.1\times {10}^{-31}\times 2.188\times {10}^6}$
$=3.3\times {10}^{-10}m$
Orbital angular momentum $=\sqrt{l(l+1)}\frac{h}{2\pi }$
$=\sqrt{l(l+1)}\frac{h}{2\pi }$ $(\because l=1for2p)$
$=\sqrt{2}\frac{h}{2\pi }$.