Question

(a) Calculate velocity of electron in first Bohr orbit of hydrogen atom (Given, $r=a_0$ ).
(b) Find de-Broglie wavelength of the electron in first Bohr orbit.
(c) Find the orbital angular momentum of $2p$-orbital in terms of $h/2\pi$ units.

Answer 1

$mvr=\frac{nh}{2\pi }$
$\Rightarrow v=\frac{nh}{2\pi mr}=\frac{6.625\times 10^{-34}}{2\times 3.14\times 9.1\times 10^{-31}\times 0.529\times 10^{-10}}$
$=2.18\times 10^{6}m{s}^{-1}$
(b) $\lambda =\frac{h}{mv}=\frac{6.625\times 10^{-34}}{9.1\times 10^{-31}\times 2.18\times 10^6}=0.33\times 10^{-9}m$
(c) Orbital angular momentum
$(L)=\sqrt{l(l+1)}\frac{h}{2\pi }=\sqrt{2}(\frac{h}{2\pi }$
$[\because$ For $p$-orbital, $l=1]$