Chapter 1.8, Problem 28P

Clouds of hot, luminous interstellar hydrogen gas can be seen in some parts of the galaxy. In some hydrogen atoms, electrons are excited to quantum levels with n = 100 or higher. (a) Calculate the wavelength observed on Earth if the electrons fall from the level with n = 100 to one with n = 2. (b) In what series would this transition be found? (c) Some of these high-energy electrons fall into intermediate states, such as n = 90. Would the wavelengths of a transition from the state with n = 100 to one with n = 90 be longer or shorter than those in the Balmer series? Explain your answer.

In the spectroscopic technique known as photoelectron spectroscopy (PES), ultraviolet radiation is directed at an atom or molecule. Electrons are ejected from the valence shell and their kinetic energies are measured. Since the energy of the incident ultraviolet photons is known and the kinetic energy of the ejected electron is measured, the ionization energy, I, can be deduced because total energy is conserved. (a) Show that the velocity, v, of the ejected electron and the frequency, n, of the incident radiation are related by hv = I + (1/2)mv^2? (b) Use this relation to calculate the ionization energy of a rubidium atom, knowing that light of wavelength 58.4 nm produces electrons with a velocity of 2,450 km/s Recall that 1 J = 1 kg.m^2/s^2

I) In Millikan's experiment, each droplet observed by the technicians contained an even number of electrons. If they had been unaware of this limitation, how would it have affected their report of an electron's charge?II) Millikan measured the charge of an electron in electrostatic units, esu. The data he collected included the following series of charges found on oil drops: 9.60 X 10^-10 esu, 1.92 X 10^-9 esu; 2.40 X 10^-9 esu; 2.88 X 10^-9 esu; and 4.80 X 10^-9 esu. (a) From this series, find the probable charge of the electron in electrostatic units. (b) Estimate the number of electrons in an oil drop with a charge of 6.72 X 10^-9 esu. The actual charge (in Coulombs) of an electron is 1.602 X 10^-19 C. What is the relationship between esu and Coulombs?