# Worksheet: Quantum Particle in a Potential Well

In this worksheet, we will practice finding stationary solutions of the Schrödinger wave equation and calculating the energy states of bound particles.

**Q10: **

Assume that a proton in a nucleus can be treated as if it were confined to a one-dimensional box of width 12.0 fm.

What is the energy of the proton when it is in the state corresponding to ?

- A J
- B J
- C J
- D J
- E J

What is the energy of the proton when it is in the state corresponding to ?

- A J
- B J
- C J
- D J
- E J

What is the energy of the photon emitted when the proton makes the transition from the first excited state to the ground state?

- A J
- B J
- C J
- D J
- E J

What is the energy of the photon emitted when the proton makes the transition from the second excited state to the ground state?

- A J
- B J
- C J
- D J
- E J

**Q12: **

An electron in a box is in the ground state with energy 1.50 eV.

Find the width of the box.

How much energy is needed to excite the electron to its first excited state?

If the electron makes a transition from an excited state to the ground state with the simultaneous emission of 20.0 eV photon, find the quantum number of the excited state.

**Q15: **

An electron is confined to a metal cube of side length 0.60 cm. The density of states for the electron in the cube varies with the electron’s energy.

Find the density of states for .

- A m
^{−3}⋅J^{−1} - B m
^{−3}⋅J^{−1} - C m
^{−3}⋅J^{−1} - D m
^{−3}⋅J^{−1} - E m
^{−3}⋅J^{−1}

Find the density of states for .

- A m
^{−3}⋅J^{−1} - B m
^{−3}⋅J^{−1} - C m
^{−3}⋅J^{−1} - D m
^{−3}⋅J^{−1} - E m
^{−3}⋅J^{−1}

Find the density of states for .

- A m
^{−3}⋅J^{−1} - B m
^{−3}⋅J^{−1} - C m
^{−3}⋅J^{−1} - D m
^{−3}⋅J^{−1} - E m
^{−3}⋅J^{−1}