PHZ3400-09 Problem Set 1

Problem 1

a) Briefly describe how the study of blackbody radiation led to Planck’s quantum hypothesis.

b) Derive Wien’s law from Planck’s radiation formula.

c) Derive the Stefan-Boltzmann law from Planck’s radiation formula.

Use: $\int _{o}^{\infty }[x^{3}/[e^{x}-1]dx=\pi ^{4}/15.$

Problem 2

a) Derive a (non-relativistic) expression for the de Broglie wavelength (in nanometers) of an electron in terms of the potential difference V (in volts) through which it has been accelerated.

b) A scanning electron microscope (SEM) at MARTECH uses an electron beam of energy of 30 keV. What is the smallest feature that can possibly be resolved with this SEM?

c) Estimate the de Broglie wavelength of yourself when you are walking at a brisk pace. Discuss the result.

Problem 3.

Suppose that the interaction energy between two atoms is given by:

$E(R)=-{\frac {A}{R^{2}}}+{\frac {B}{R^{10}}}$

The atoms form a stable molecule with an inter- nuclear distance of 0.3nm and a dissociation energy of 4 eV.

a) Determine A and B.

b) Calculate the force required to break the molecule. What is the critical distance between the nuclei for which this occurs?