Exam 39: More About Matter Waves

The figure shows the energy levels for an electron in a finite potential energy well. If an electron in the n = 2 state absorbs a photon of wavelength 2.0 nm, what happens to the electron?

The ground state energy of an electron in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is 2.0 eV. If the width of the well is doubled, the ground state energy will be:

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton. Then, according to the quantum theory the energy E_n of a state with principal quantum number n is proportional to:

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton. Then the ground state energy of a hydrogen atom is -13.6 eV. The minus sign indicates:

A particle is confined to a one-dimensional trap by infinite potential energy walls. Of the following states, designed by the quantum number n, for which one is the probability density greatest near the center of the well?

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton. Then the ground state energy of a hydrogen atom is -13.6 eV. When the electron is in the first excited state its excitation energy (the difference between the energy of the state and that of the ground state) is:

An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls. A graph of its wave function $\Psi$ (x) versus x is shown. The value of quantum number n is:

The wave function for an electron in a state with zero angular momentum:

A particle is trapped in an infinite potential energy well. It is in the state with quantum number n = 14. How many nodes does the probability density have (counting the nodes at the ends of the well)?

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton. Then the ground state energy of a hydrogen atom is -13.6 eV. The energy of the first excited state is:

A particle is confined by finite potential energy walls to a one-dimensional trap from x = 0 to x = L. Its wave function in the region x > L has the form:

The figure shows the energy levels for an electron in a finite potential energy well. If the electron makes a transition from the n = 3 state to the ground state, what is the wavelength of the emitted photon?

The following image is a dot plot of the ground state of the hydrogen atom. The dots represent:

A particle is trapped in a one-dimensional well with infinite potential energy at the walls. Three possible pairs of energy levels are Order these pairs according to the difference in energy, least to greatest.

If the wave function $\Psi$ is spherically symmetric then the radial probability density is given by:

Consider the following: Of these which are spherically symmetric?

If a wave function $\Psi$ for a particle moving along the x axis is "normalized" then:

An electron in an atom initially has an energy 5.5 eV above the ground state energy. It drops to a state with energy 3.2 eV above the ground state energy and emits a photon in the process. The wave associated with the photon has a wavelength of:

The Balmer series of hydrogen is important because it:

The radial probability density for the electron in the ground state of a hydrogen atom has a peak at about: