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Chapter 40: Q. 30 (page 1176)
a. Derive an expression for , the wavelength of light emitted by a particle in a rigid box during a quantum jump from
b. In what length rigid box will an electron undergoing a transition emit light with a wavelength of ? This is the wavelength of a ruby laser
a.
b.
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a. What is the probability that an electron will tunnel through aair gap from a metal to a STM probe if the work function is ?
b. The probe passes over an atom that is“tall.” By what factor does the tunneling current increase?
c. If a current change is reliably detectable, what is the smallest height change the STM can detect?
A neutron is confined in a -diameter nucleus. If the nucleus is modeled as a one-dimensional rigid box, what is the probability that a neutron in the ground state is less than from the edge of the nucleus?
Even the smoothest mirror finishes are “rough” when viewed at a scale of . When two very smooth metals are placed in contact with each other, the actual distance between the surfaces varies fromat a few points of real contact to . The average distance between the surfaces is. The work function of aluminum is . What is the probability that an electron will tunnel between two pieces of aluminum that are apart? Give your answer as a power ofrather than a power of.
Sketch the wave function for the potential energy shown in FIGURE EX40.14.
In most metals, the atomic ions form a regular arrangement called a crystal lattice. The conduction electrons in the sea of electrons move through this lattice. FIGURE CPis a one-dimensional model of a crystal lattice. The ions have mass , charge and an equilibrium separation .
a. Suppose the middle charge is displaced a very small distance from its equilibrium position while the outer charges remain fixed. Show that the net electric force on the middle charge is given approximately by
In other words, the charge experiences a linear restoring force.
b. Suppose this crystal consists of aluminum ions with an equilibrium spacing of . What are the energies of the four lowest vibrational states of these ions?
c. What wavelength photons are emitted during quantum jumps between adjacent energy levels? Is this wavelength in the infrared, visible, or ultraviolet portion of the spectrum?
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