(a) find the energy of the ground state (n = 1) and the first two excited states of an electron in a one-dimensional box of length l = 1.0 10-15 m = 1.00 fm (about the diameter of an atomic nucleus). ground state mev first excited state mev second excited state gev make an energy-level diagram for the system. (do this on paper. your instructor may ask you to turn in this work.) (b) calculate the wavelength of electromagnetic radiation emitted when the electron makes a transition from n = 2 to n = 1. fm (c) calculate the wavelength of electromagnetic radiation emitted when the electron makes a transition from n = 3 to n = 2. fm (d) calculate the wavelength of electromagnetic radiation emitted when the electron makes a transition from n = 3 to n = 1. fm

(a)

The energy levels of an electron in a box are given by

where

n is the energy level

is the Planck constant

is the mass of the electron

is the size of the box

Substituting n=1, we find the energy of the ground state:

Converting into MeV,

Substituting n=2, we find the energy of the first excited state:

Converting into MeV,

Substituting n=3, we find the energy of the second excited state:

Converting into GeV,

(b)

The energy of the emitted radiation is equal to the energy difference between the two levels, so:

And the energy of the electromagnetic radiation is

where c is the speed of light; so, re-arranging the formula, we find the wavelength:

(c)

The energy of the emitted radiation is equal to the energy difference between the two levels, so:

Using the same formula as before, we find the corresponding wavelength:

(d)

The energy of the emitted radiation is equal to the energy difference between the two levels, so:

Using the same formula as before, we find:

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