Figure 39-26 indicates the lowest energy levels (in electron-volts) for five sit

Question

Figure 39-26 indicates the lowest energy levels (in electron-volts) for five situations in which an electron is trapped in a one-dimensional infinite potential well. In wells B, C, D, and E, the electron is in the ground state. We shall excite the electron in well A to the fourth excited state (at 25 eV). The electron can then de-excite to the ground state by emitting one or more photons, corresponding to one long jump or several short jumps. Which photon emission energies of this de-excitation match a photon absorption energy (from the ground state) of the other four electrons? Give the n values. [Note: The second excited state of well B should have an energy of 18 eV instead of 19 eV.]

Explanation / Answer

For A:

a) n=5 to n=4

E5 - E4 = 25 - 16 = 9eV

ans. D; n = 1 to n = 2

b) n=5 to n=3

E5 - E3 = 25 - 9 = 16eV

ans. B n=1 to n=3

c) n=5 to n=2;

25 - 4 = 21

ans. none

d) n=5 to n=1

25 - 1 = 24eV

ans. D; n=1 to n=3

e) n=4 to n=3

16 - 9 = 7eV

ans. none

f) n=4 to n=2

16 -4 = 12eV

ans. C; n=1 to n=2

g) n=4 to n=1

16 - 1 = 15eV

ans. D; n=2 to n=3

h) n=3 to n=2

9-4 = 5eV

ans. none

i) n=3 to n=1

9-1 = 8eV

ans. none

j) n=2 to n=1

4-1 = 3eV

ans. none

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