Question

If an electron is confined to one-dimensional motion between two infinite potential walls which are separated by a distance equal to the Bohr radius, calculate the energies of the three lowest states of motion. Calculate numerical value of ground state energy and compare it with hydrogen atom ground state energy.

Answer #1

If an electron is confined to one-dimensional motion
between two infinite potential walls which are separated by a
distance equal to Bohr radius, calculate energies of the three
lowest states of motion.Calculate numerical value of ground state
energy and compare it with hydrogen atom ground state energy.

1. As we increase the quantum number of an electron in a
one-dimensional, infinite potential well, what happens to the
number of maximum points in the probability density function?
It increases.
It decreases.
It remains the same
2. If an electron is to escape from a one-dimensional, finite
well by absorbing a photon, which is true?
The photon’s energy must equal the difference between the
electron’s initial energy level and the bottom of the nonquantized
region.
The photon’s energy must...

1. An electron is confined to a region of size 0.15 nm (i.e.,
infinite potential walls at either end). (a) (5 pts) What is the
ground state energy in eV? (b) (5 pts) The electron falls from the
5th excited state to the 3rd excited state, emitting a photon in
the process. What is the wavelength of the photon in nm?
2. Refer to the previous problem. (a) (4 pts) When the electron
is in the 5th excited state, at...

A particle is confined to the one-dimensional infinite potential
well of the figure. If the particle is in its ground state, what is
the probability of detection between x = 0.20L
and x = 0.65L?

Eight electrons are confined to a two-dimensional infinite
potential well with widths L_X = L y =L. Assume that the electrons
do not electrically interact with one another. Considering electron
spin and degeneracies of some energy levels, what is the total
energy of the eight-electron system in its ground state, as a
multiple of h^2/(8mL^2 )?

Consider a particle trapped in an infinite square well potential
of length L. The energy states of such a particle are given by the
formula: En=n^2ℏ^2π^2 /(2mL^2 ) where m is the mass of the
particle.
(a)By considering the change in energy of the particle as the
length of the well changes calculate the force required to contain
the particle. [Hint: dE=Fdx]
(b)Consider the case of a hydrogen atom. This can be modeled as
an electron trapped in an infinite...

Consider the Bohr model of the hydrogen atom for which an
electron in the ground state executes uniform circular motion about
a stationary proton at radius a0. (a) Find an expression
for the kinetic energy of the electron in the ground state. (b)
Find an expression for the potential energy of the electron in the
ground state. (c) Find an expression for the ionization energy of
an electron from the ground state of the hydrogen atom. The
ionization energy is...

II(20pts). Short Problems
a) The lowest energy of a particle in an infinite one-dimensional
potential well is 4.0 eV. If the width of the well is doubled, what
is its lowest energy?
b) Find the distance of closest approach of a 16.0-Mev alpha
particle incident on a gold foil.
c) The transition from the first excited state to the ground
state in potassium results in the emission of a photon with = 310
nm. If the potassium vapor is...

A proton, a neutron, and an electron are trapped in identical
one-dimensional infinite potential wells; each particle in its
ground state.
a.) At the center of the wells, is the probability density for
the proton greater than, less than, or equal to that of the
electron? Explain.
b.) At the center of the wells, is the probability density for
the neutron greater than, less than, or equal to that of the
electron? Explain.

An electron is confined to a 1 micron (1.00 x 10-6m)
thin layer of silicon. Assuming that the silicon can be described
by a one-dimensional box with infinite potential walls, calculate
the lowest possible energy within the material. The effective mass
of electrons in silicon is m* = 2.37 x 10-31
kg.

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