Question

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* = 0.072 nm?
p =

4) Now, assume the electron is in the energy eigenstate that is
the closest in energy to that of the ground state. What is the
probability that the electron in this state is located within the
region between *x* = 0.048 nm and *x* = 0.072 nm? p
=

Answer #1

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...

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...

4.
An electron is trapped in a one-dimensional infinite potential well
of width L.
(1) Find wavefunction ψn(x) under assumption that the
wavefunction in 1 dimensional box whose potential energy U is 0 (0≤
z ≤L) is normalized
(2) Find eighenvalue En of electron
(3) If the yellow light (580 nm) can excite the elctron from
n=1 to n=2 state, what is the width (L) of petential well?

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

An infinitely deep square well has width L = 2.5 nm.
The potential energy is V = 0 eV inside the well
(i.e., for 0 ≤ x ≤ L). Seven electrons
are trapped in the well.
1) What is the ground state (lowest) energy of this seven
electron system in eV?
Eground =
2) What is the energy of the first excited state of the system
in eV?
NOTE: The first excited state is the one that has the lowest...

An electron is trapped in a one-dimensional infinite well. The
largest wavelength emitted by the electron is 650 nm. a) Determine
the width of the well.
how do you find the 3rd largest wavelength

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 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?

A particle is confined to the one-dimensional infinite potential
well of width L. If the particle is in the
n=2 state, what is its probability of detection between a) x=0, and
x=L/4; b) x=L/4, and x=3L/4; c) x=3L/4,
and x=L? Hint: You can double check your answer if you calculate
the total probability of the particle being
trapped in the well.
Please answer as soon as possible.

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...

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