Question

(a) Calculate the radii of the first three Bohr orbits for hydrogen.

(Planck's constant $h=6.6262\times {10}^{-34}$ J s; mass of electron $m=9.1091\times {10}^{-31}$ kg; charge on electron $e=1.60210\times {10}^{-19}$ C; permittivity of vacuum ${ϵ}_0=8.854185\times {10}^{-12}{C}^2{N}^{-1}{m}^{-2}$. )
(b) Use these radii to calculate the velocity of an electron in each of these three orbits.

Answer 1

Radius of an hydrogen atom in bohr's orbit is given by,

$r_n=0.529\times \left(n^2\right)A^0$

Therefore for,

$n=1$, $r_1=0.529A^0$

$n=2$, $r_2=2.12A^0$

$n=3$, $r_3=4.77A^0$

Velocity of an hydrogen atom in bohr's orbit is given by,

$v_n=\frac{2.165\times {10}^{6}m/s}{\left(n\right)}$

For $n=1$, $v_1=2.165\times {10}^{6}m/s$

For $n=2$, $v_2=1.82\times {10}^{6}m/s$

For $n=3$, $v_3=7.216\times {10}^{5}m/s$