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Modern physics: photon energies, wavelengths, oscillators, etc.

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2An atom of mass 2.66 ✕ 10-26 kg oscillates in one dimension at a frequency of 0.60 ✕ 1013 Hz. What is its effective force constant?

What are its quantized energy levels?

3. A H2 molecule can be approximated by a simple harmonic oscillator having a spring constant k = 1.1 ✕ 103 N/m.
(a) How many different energy transitions are possible when the H2 molecule decays from the third excited state down to the ground state?

(b) Find the photon energies produced in these transitions and their wavelengths.

4. Let 10.0 eV electrons approach a potential barrier of height 4.4 eV.
(a) For what minimum barrier thickness is there no reflection?
(b) For what minimum barrier thickness is the reflection a maximum?

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(1)
In a simple harmonic oscillator, the angular frequency of the oscillator is given as a function of the spring constant k and the mass m:
(1.1)
Thus:
(1.2)
Since where f is the linear frequency, we get:
(1.3)
In our case:


(2)
The energy levels of one dimensional harmonic oscillator are:
(1.4)
Where is the reduced Planck constant.
In our case:


(3)
There are three possible decay energy transition from the third (n=3) excited state, as ...

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