Question

An electron is bound to a region within a crystal by a springlike force having an effective spring constant of 150 ev/nm2.

(a) Find the ground state energy in eV.

(b) If the electron drops from the 3rd excited state to the 1st excited state, what is the wavelength of the emitted photon?

(c) At what total energy in eV will the turnaround distance be 1.5 nm?

Answer #1

a]

For a spring system, the angular frequency of its motion is related to its spring's constant and mass as:

k = 150 eV/nm^{2} = 24 N/m

so,

therefore, ground state energy is:

b] When the electron drops from 3rd to 1st excited state, the difference in the energy of the states = energy of the photon emitted.

=>

c] E = (1/2)kx^{2}

E = 337.5 eV.

this is energy for which the turnaround distance is 1.5nm.

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