Exam 39: More About Matter Waves

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 probability density P(x) versus x is shown. The value of the quantum number n is:

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

If P(r) is the radial probability density for a hydrogen atom then the probability that the separation of the electron and proton is between r and r + dr is:

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and porton. 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 is:

A particle in a certian finite potential energy well can have any of five quantized energy values and no more. Which of the following would allow it to have any of six quantized energy levels?

A particle is trapped in a finite potential energy well that is deep enough so that the electron can be in the state with n = 4. For this state how many nodes does the probability density have?

When a hydrogen atom makes the transition from the second excited state to the ground state (at -13.6 eV) the energy of the photon emitted is:

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

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

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:

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:

The quantum number n is most closely associated with what property of the electron in a hydrogen atom?

Four different particles are trapped in one-dimensional wells with infinite potential energy at their walls. The masses of the particles and the width of the wells are Rank them according to the kinetic energies of the particles when they are in their ground states.

An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls. The ratio E₃/E₁ of the energy for n = 3 to that for n = 1 is:

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

The binding energy of an electron in the ground state in a hydrogen atom is about:

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

An electron is in a one-dimensional well with finite potential energy barriers at the walls. The matter wave:

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?