Consider hydrogen in the ground state, 100 . (a) Use the derivative to determine the radial position for which the probability density, P(r), is a maximum. (b) Use the integral concept to determine the average radial position. (This is called the expectation value of the electrons radial position.) Express your answers into terms of the Bohr radius, a0. Hint: The expectation value is the just average value, (c) Why are these values different?

The valence election of chlorine is excited to a 3p state, (a) What is the magnitude of the election's orbital angular momentum? (b) What are possible values for the z-component of angular’ measurement?

Question 3: Consider electron and vibrational (nuclear) dynamics of a metal cluster that consists of Au- S bonds. The cluster is spherical, with spatial confinement of one nanometer. If the cluster is excited using 800-nm, how long would it take for an electron to move one nanometer (i.e. across the cluster)? How long would it take for one of the sulfur atoms to move the same distance?

Write down for yourself the expression for the radial distribution function of a 2s electron in a hydrogenic atom and determine the radius in Angstroms at which the electron is most likely to be found. Assume the species has an atomic number of 2. (Ans. in Agstroms)

One can now use integrated-circuit technology to manufacture a "box" that traps electrons in a region only a few nanometers wide. Imagine that we make an essentially one-dimensional box with a length of 3 nanometers. Suppose we put 10 electrons in such a box and allow them to settle into the lowest possible energy states consistent with the Pauli exclusion principle. a) What will be the value of the highest energy level occupied by at least one electron? b) What will be the electrons' total energy (ignoring their electrostatic repulsion)? c) How would your answers to the above be different if the electrons were bosons instead of fermions? d) What is the wavelength of the lowest energy photon that can be absorbed (the electrons in this box are fermions)?

Is it possible to reverse the Boltzmann population? What is the usefulness of such a condition? Explain why 4 state laser is more useful than 3 state lasers?

The distance r between the electron and the nucleus in a hydrogenatom (in its lowest energy state) is a random variable with probability density p(r) = 4a03r2e- 2r/ao for r > 0, where ao is the Bohr radius (Figure 8). Calculate the probability P that the electron is within one Bohrradius of the nucleus. The value of a0 is approximately 5.29 x 10- 11 m,but this value is not needed to compute P.

The Morse potential The harmonic potential, V(x) = ½kx?, is useful start for modelling molecular vibrations, but it has limitations. A realistic potential between to atoms should accurately represent the sharp increase in the potential as two nuclei come in close proximity, and also have the ability for a bond to break: that is, an asymptote V →0 as x →00. One option, as shown in the figure, is the Morse potential: V(r) = D(1 – e-«(r=re))2 15 10 10 15 20 The parameter D is the well depth (or binding energy) of the potential, re is the bond length, and a is the anharmonicity constant.

How would I be able to solve Problem 11.23? The chapter that this problem is in is called "Atomic transitions and radiation." The section it resides in is named Atomic Selection Rules.