**Q3: **

A billiard ball of mass 0.200 kg bounces back and forth between the cushions of a 1.50 m long table. No energy is lost during the ball’s motion or during its collisions with the cushions.

If the ball is in its ground state, how many years does it take to move from one cushion to the other?

- A
- B
- C
- D
- E

How much energy is required to excite the ball from its ground state to its first excited state?

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

**Q4: **

Atoms in a crystal lattice vibrate in simple harmonic motion. What is the force constant of the lattice if a lattice atom makes a transition from the ground state to first excited state when it absorbs a 525-μm photon? Use a value of kg for the mass a lattice atom.

**Q5: **

A quantum harmonic oscillator makes a transition from the state to the state and emits a photon that has a wavelength of 0.450 μm. What is the oscillator’s frequency?

- A Hz
- B Hz
- C Hz
- D Hz
- E Hz