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 $2 p$-orbital in terms of $h / 2 \pi$ units.

Answer 1

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