Exam 39: Quantum Mechanics

An electron is in an infinite square well (a box) that is 8.9 nm wide. What is the ground state energy of the electron? (h = 6.626 × 10^-34 J ∙ s, ^mel = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

An electron with kinetic energy 2.80 eV encounters a potential barrier of height 4.70 eV. If the barrier width is 0.40 nm, what is the probability that the electron will tunnel through the barrier? (1 eV = 1.60 × 10^-19 J, mel = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s)

An electron is confined in a harmonic oscillator potential well. What is the longest wavelength of light that the electron can absorb if the net force on the electron behaves as though it has a spring constant of 74 N/m? (^mel = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J, = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

The wave function of an electron in a rigid box (infinite well) is shown in the figure. If the electron energy 98.0 eV, what is the energy of the electron's ground state? ( ^mel = 9.11 × 10^-31 kg)

You want to confine an electron in a box (an infinite well) so that its ground state energy is 5.0 × 10^-18 J. What should be the length of the box? (h = 6.626 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg)

An electron is bound in an infinite square-well potential (a box) on the x-axis. The width of the well is L and the well extends from x = 0.00 nm to x = 3.8 nm. In its present state, the normalized wave function of the electron is given by: ψ(x) = sin (2πx/L). What is the energy of the electron in this state? (h = 6.626 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

Find the value of A to normalize the wave function ψ(x) = .

A particle is confined to a one-dimensional box (an infinite well) on the x-axis between x = 0 and x = L. The potential height of the walls of the box is infinite. The normalized wave function of the particle, which is in the ground state, is given by ψ(x) = sin , with 0 ≤ x ≤ L. What is the maximum probability per unit length of finding the particle?

A lithium atom, mass 1.17 × 10-⁻²⁶ kg, vibrates with simple harmonic motion in a crystal lattice, where the effective force constant of the forces on the atom is k = 49.0 N/m. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10⁻³⁴ J ∙ s, = 1.055 × 10⁻³⁴ J ∙ s, 1 eV = 1.60 × 10⁻¹⁹ J) (a) What is the ground state energy of this system, in eV? (b) What is the wavelength of the photon that could excite this system from the ground state to the first excited state?

An 80-eV electron impinges upon a potential barrier 100 eV high and 0.20 nm thick. What is the probability the electron will tunnel through the barrier? (1 eV = 1.60 × 10^-19 J, mproton = 1.67 × 10^-27 kg, = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

Find the wavelength of the photon emitted during the transition from the second EXCITED state to the ground state in a harmonic oscillator with a classical frequency of 3.72 × 10¹³ Hz. (c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J, = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

The probability density for an electron that has passed through an experimental apparatus is shown in the figure. If 4100 electrons pass through the apparatus, what is the expected number that will land in a 0.10 mm-wide strip centered at x = 0.00 mm?

A set of five possible wave functions is given below, where L is a positive real number. Ψ1(x) = Ae^-x, for all x ψ2(x) = A cos x, for all x Ψ3(x) = Ψ4(x) = Ψ5(x) = Which of the five possible wave functions are normalizable? (There may be more than one correct choice.)

The energy of a particle in the second EXCITED state of a harmonic oscillator potential is What is the classical angular frequency of oscillation of this particle? (1 eV = 1.60 × 10^-19 J, = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s)

Find the value of A to normalize the wave function ψ(x) = .

The wave function for an electron that is confined to x ≥ 0 nm is ψ(x) = (a) What must be the value of A? (b) What is the probability of finding the electron in the interval 1.15 nm ≤ x ≤ 1.84 nm?

A particle confined in a rigid one-dimensional box (an infinite well) of length 17.0 fm has an energy level E_n = 24.0 MeV and an adjacent energy level E_n+1= 37.5 MeV. What is the value of the ground state energy? (1 eV = 1.60 × 10^-19 J)

The lowest energy level of a certain quantum harmonic oscillator is 5.00 eV. What is the energy of the next higher level?

A 10.0-g bouncy ball is confined in a 8.3-cm-long box (an infinite well). If we model the ball as a point particle, what is the minimum kinetic energy of the ball? (h = 6.626 × 10^-34 J ∙ s)

An electron is bound in an infinite well (a box) of width 0.10 nm. If the electron is initially in the n = 8 state and falls to the n = 7 state, find the wavelength of the emitted photon. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg)