10.3.P1

In chemistry one occasionally uses a flame test to determine the presence of certain chemicals. If we put a small spoon with sodium in it into a Bunsen burner flame just above the tip (T ~ 1500 K) it will glow with a characteristic yellow color. In this problem we’ll work out about how many atoms of sodium are responsible for what we see. We’ll assume that as the sodium is heated, collisions with hot molecules drive the outermost electron of some of the sodium atoms up from its ground state (labeled 3s) to its first excited state (labeled 3p). The flame and the energy levels of the least bound electron in sodium are shown in the figure at the right. (Don’t worry about the complexity of the diagram, we only need the two levels involved in the 3p-3s transition indicated by the yellow arrow.)

A. The wavelength of the yellow light emitted by the 3p-3s transition in sodium is 590 nm. What is the energy of the emitted photon (in electron volts)?

B. At room temperature (T ~ 300 K), what is the probability that a sodium atom has its electron excited up to the 3p state?

C. At the temperature of the flame (T ~ 1500 K), what is the probability that a sodium atom has its electron excited up to the 3p state?

D. If we have 1 gram of sodium in our spoon, about how many atoms in the burner flame have their electron excited up to the 3p state at any one time? (Possibly useful fact: the atomic weight of sodium is 23 Da = 23 AMU.)

Joe Redish 5/21/12