# 1. Photon and Matter Waves 2. Compton Effect

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34

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stop

0

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stop

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e

X

2

2

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50μm

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2 2 2

2 2 2

2 2 2

2 2

2

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2 2 2

2 2 2 2

2 2 2

2

2

2 2

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n

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2 2

2

n

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2 2 2

2

pot

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2 2

2

bL

b

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t t

t

2 2 2

n

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## 量子圍欄

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39-

Fig. 39-16

2 2

### L n   n  

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Coulomb force attracting electron toward nucleus

39- 1 2

2

2 2

2 0

###  

Quantize angular momentum

###  

Substitute v into force equation

2 0 2

2

2

### , for n  1, 2,3, 

Where the smallest possible orbital radius (n=1) is called the Bohr radius a:

2 0 10

2

### 

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The total mechanical energy of the electron in H is:

39- 2 2

12 2

0

###  

Solving the F=ma equation for mv2 and substituting into the energy equation above:

2

0

###  

Substituting the quantized form for r:

4

2 2 2 0

n

18

2 2

n

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### Energy Changes

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Substituting f=c/ and using the energies En allowed for H:

2 2

low high

high low

4

2 3 2 2

0 high low

###         

Where the Rydberg constant

4 7 -1

2 3 0

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2

0

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### Quantum Numbers for the Hydrogen Atom

For ground state, since

=1 l=0 and →

l =0

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Fig. 39-21

Fig. 39-20 39-

2

### 

Probability of finding electron within a small volume at a given position

Probability of finding electron within a within a small distance from a given radius

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39-

Fig. 39-25

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## References

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