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Emission spectrum of hydrogen

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Why were electrons limited
in the energies they can possess?

 

 

 

 

Electron Standing Waves

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| Onsite Version |

St. Mary's U. Astronomy and Physics Dept.

 

 

 

 

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

 

 

 

5 wavelengths

 

 

 

 

 

 

 

 

4 wavelengths

 

 

 

 

 

 

 

File:DB3.png

 

3 wavelengths

 

 

 

 

File:DB2.png

 

2 wavelengths

 

 

 

 

 

 

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

 

 

Electron Wave/Bohr

Monterey Institute for Technology and Education

 

 

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∏

 

 

 

Limitations

 

 

 

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