# Problems in Quantum Mechanics

1. The wavelength spectrum of the radiation energy emitted from a system in thermal equilibrium is observes to have a maximum value which decreases with increasing temperature. Outline briefly the significance of this observation for quantum physics.

2. The “stopping potential” in a photoelectric cell depends only on the frequency v of the incident electromagnetic radiation and not on its intensity. Explain how the assumption that each photoelectron is emitted following the absorption of a single quantum of energy hv is consistent with this observation.

3. Write down the de Broglie equations relating the momentum and energy of free particle to, respectively, the wave number k and angular frequency w of the wave-function which describes the particle.

4. Write down the Heisenberg uncertainty Principle as it applies to the position x and momentum p of a particle moving in one dimension.

5. Estimate the minimum range of the momentum of a quark confined inside a proton size 10 ^ -15 m.

6. Explain briefly how the concept of wave-particle duality and the introduction of a wave packet for a particle satisfies the Uncertainty Principle.

#### Solution Summary

We solve several problems in quantum mechanics.