(a) What are the energies of the first three energy levels of an electron confin

Question

(a) What are the energies of the first three energy levels of an electron confined in a one-dimensional box of length 0.78 nm?
___J (lowest energy level)
___J (next-lowest energy level)
___J (next-lowest energy level)

(b) How much energy must the electron lose to move from the n = 3 energy level to the n = 1 energy level?
___J

(c) Suppose that an electron can move from the n = 3 level to the n = 1 level by emitting a photon of light. If energy is conserved, what must the photon's wavelength be?
___nm

Explanation / Answer

(a) E1 = h2 / 8mL2

= 3.77 x 10-19 eV-m2 / L2

Substitute L = 0.78 nm

E1 = 3.77 x 10-19 eV-m2 / 0.782 x 10-18

= 0.6196 eV

Next lowest level is 4E1 = 4 * 0.6196 = 2.478 eV

Next lowest level is 9E1 = 9 * 0.6196 = 5.5764 eV

(b) energy lose = E3 - E1 = 5.5764 - 0.6196 = 4.9568 eV

(c) E3 - E1 = hc / lambda

lambda = h c / E3 - E1

= 6.626 x 10-34 * 3 x 108 / 4.9568 x 1.6 x 10-19

= 2.506 x 10-7

= 250.6 nm

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