Question

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.

Answer #1

so we found that probability density of a particle at the center of the box depends only on the size of the box but not on the masses of the particles. hence the probability density of all the three particles will be equal

a) both proton and electron probability density equal

b) both electron and neutron probability density equal.

For a particle trapped in a one-dimensional infinite square well
potential of length ?, find the probability that the particle is in
its ground state is in
a) The left third of the box: 0 ≤ ? ≤ ?/3
b) The middle third of the box: ?/3 ≤ ? ≤ 2?/3
c) The right third of the box: 2?/3 ≤ ? ≤ L
After doing parts a), b), and c):
d) Calculate the sum of the probabilities you got for...

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 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...

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?

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...

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

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
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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
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A particle is confined to the one-dimensional infinite potential
well of width L. If the particle is in the
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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.

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