Question

An electron is in the 4th excited state within a bound infinite square well with a finite length. It transitions to the lower state n = 3, emitting a photon of wavelength 368.0 nm.

a) Determine the width of the well.

b) Sketch the probability distribution of finding the electron in the n = 4 state, indicating where the most likely positions the particle will be found. What is the likelihood of finding the particle within the first half of the box?

Answer #1

An electron is bound in a finite square well of width 1.85 nm
and finite depth U0=6E?, where E? is the
ground-state energy for an infinitely deep potential well that has
the same width.
If the electron is initially in the ground state level of the
finite square well, E1=0.625E?, and absorbs a
photon, what maximum wavelength can the photon have and still
liberate the electron from the finite well?

An electron is bound in a finite square well of width 2.00 nm
and finite depth U0=6E?, where E?is the
ground-state energy for an infinitely deep potential well that has
the same width.
Part A
If the electron is initially in the ground state level of the
finite square well, E1=0.625E?, and absorbs a
photon, what maximum wavelength can the photon have and still
liberate the electron from the finite well?
Express your answer numerically in meters using three
significant...

An electron is in the ground state of an infinite square well.
The energy of the ground state is E1 = 1.13 eV.
(a) What wavelength of electromagnetic radiation would be needed
to excite the electron to the n = 7 state? nm
(b) What is the width of the square well? nm

Suppose that an electron trapped in a one-dimensional infinite
well of width 0.341 nm is excited from its first excited state to
the state with n = 5.
1 What energy must be transferred to the electron for this
quantum jump?
2 The electron then de-excites back to its ground state by
emitting light. In the various possible ways it can do this, what
is the shortest wavelengths that can be emitted?
3 What is the second shortest?
4 What...

An electron is trapped in an infinite one-dimensional well of
width = L. The ground state energy for this electron is 3.8
eV.
a) Calculated energy of the 1st excited state.
b) What is the wavelength of the photon emitted between 1st
excited state and ground states?
c) If the width of the well is doubled to 2L and mass is halved
to m/2, what is the new 3nd state energy?
d) What is the photon energy emitted from the...

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...

An electron is in an infinite one-dimensional square well of
width L = 0.12 nm.
1) First, assume that the electron is in the lowest energy
eigenstate of the well (the ground state). What is the energy of
the electron in eV? E =
2) What is the wavelength that is associated with this
eigenstate in nm? λ =
3) What is the probability that the electron is located within
the region between x = 0.048 nm and x =...

For the infinite square-well potential, find the probability
that a particle in its third excited state is in each third of the
one-dimensional box:
(0 ≤ x ≤ L/3)
(L/3 ≤ x ≤ 2L/3)
(2L/3 ≤ x ≤ L)

An electron is bound to a region within a crystal by a
springlike force having an effective spring constant of 150
ev/nm2.
(a) Find the ground state energy in eV.
(b) If the electron drops from the 3rd excited state to the 1st
excited state, what is the wavelength of the emitted photon?
(c) At what total energy in eV will the turnaround distance be
1.5 nm?

For the infinite square-well potential, find the probability
that a particle in its fourth excited state is in each third of the
one-dimensional box:
a) (0 ≤ x ≤ L/3)
b) (L/3 ≤ x ≤ 2L/3)
c) (2L/3 ≤ x ≤ L)

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