Question

Determine the circumference of the second Bohr orbit of the Hydrogen atom. Use this to
determine the wavelength of the electron in this orbit; the electron's wave must consist of
an integral number of wavelengths about its orbit's circumference (Why?).
orbit circumference = n wavelength

Finally, determine the velocity v of the electron in this orbit using de Broglie's prescription
for the wavelength of matter waves.
wavelength = h / mv

What percentage of the speed of light is this velocity?

Answer 1

Radius of second orbit of hydrogen atom = 0.529*n² / Z A°

= 0.529×2² = 2.116×10^-10 m

The circumference = 2 πR = 2 × 3.14 × 2.116×10^-10 m = 13.295×10^-10 m =1.33×10^-9 m (Answer)

Circumference = n × $\lambda$

$\lambda$ = circumference /2 = 6.6476×10^-10 m = 6.65×10^-10 m. (Answer)

$\lambda$ = h/mv

Velocity of electron = h/m$\lambda$ = 6.626×10^-34/(9.11×10^-31 × 6.65×10^-10 ) = 1.094×10⁶ m/s = 1.09×10⁶ m/s. (Answer)

% of velocity as speed of light =( 1.09×10⁶/3×10⁸)×100 %

= 0.3647%

= 0.36 %. (Answer)