Why were electrons limited in the energies they can possess?

1. An electron is a standing wave. (A bound wave)

2. Standing waves can only be a whole number of wavelengths

3. Limited wavelengths mean limited possible energies

Possible electron circumference

= 2∏r = nλ

where n=1,2,3,4 etc

Wavelength - describes probability of finding an electron at particular position.

Electron is a wave circled in on itself
This standing wave has four cycles

The angular (circular) momentum of an electron is limited

Because a circular electron must be a whole number of wavelengths …

Then C = 2(∏)r = nλ

where n = 1, 2, 3 etc.

And λ = h/p = h/mv

Then … 2(∏)r = nh/mv

Angular momentum =

mvr = nh/2∏

Angular momentum (mvr) is restricted to whole number
multiples of h/2∏