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Why were electrons limited
in the energies they can possess?

Electron Standing Waves

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

5 wavelengths

4 wavelengths

3 wavelengths

2 wavelengths

2. Circular standing waves can only be a whole number of wavelengths

3. Limited wavelengths mean limited possible energies

Possible Electron Circumferences

= 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 wave must be a whole number of wavelengths

Then C = 2(∏)r = nλ

where n = 1,2,3,4 etc

And λ = h/p = h/mv

Then … 2(∏)r = nh/mv

Angular Momentum

mvr = n[h/2∏]

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