Exam 39: More About Matter Waves

Two one-dimensional traps have infinite potential energy at their walls. Trap A has width L and trap B has width 2L. For which value of the quantum number n does a particle in trap B have the same energy as a particle in the ground state of trap A?

An electron confined in a one-dimensional infinite potential well has an energy of 180 eV. What is its wavelength?

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:

An electron in an atom initially has an energy 7.5 eV above the ground state energy. It drops to a state with an energy of 3.2 eV above the ground state energy and emits a photon in the process. The momentum of the photon is:

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, lowest to highest.

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 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?

Identical particles are trapped in one-dimensional wells with infinite potential energy at the walls. The widths L of the traps and the quantum numbers n of the particles are Rank them according to the kinetic energies of the particles, least to greatest.

A particle in a certain 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?

An electron is trapped in a deep well with a width of 0.3 nm. If it is in the state with quantum number n = 3 its kinetic energy is:

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

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

An electron in an atom drops from an energy level at -1.1 *10^-18 J to an energy level at -2.4 * 10^-18 J. The wave associated with the emitted photon has a frequency of:

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

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:

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:

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:

Which of the following sets of quantum numbers is possible for an electron in a hydrogen atom?

The diagram shows the energy levels for an electron in a certain atom. Of the transitions shown, which represents the emission of a photon with the most energy?

The series limit for the Balmer series represents a transition m $\rightarrow$ n, where (m, n) is