Question

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* ≤ 2*L*/3)

c) (2*L*/3 ≤ *x* ≤ *L*)

Answer #1

The wave function of the particle in fourth excited state (n = 5) is

The probability density is square of wave function

The integration of the of the probability density gives

a) Therefore probability for the particle to be from x = 0 to x = L/3 is

b) probability for the particle to be from x = L/3 to x = 2L/3 is

c) probability for the particle to be from x = 2L/3 to x = L is

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)

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...

A particle is in the ground state of an infinite square well.
The potential wall at x = L suddenly (i.e., instantaneously) moves
to x = 3L. such that the well is now three times its original size.
(a) Let t = 0 be at the instant of the sudden change in the
potential well. What is ψ(x, 0)?
(b) If you measure the energy of the particle in the new well,
what are the possible energies?
(c) Estimate the...

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.

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?

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...

Consider a three dimensional rectangular infinite potential well
with sides of length L, 2L and 3L.
What is the energy of the first excited state relative to the
energy of the ground state?
What is the energy of the second excited state relative to the
energy of the ground state?
What is the energy of the third excited state relative to the
energy of the ground state?
What is the energy of the fourth excited state relative to the
energy...

Considera particle in the ground state of an infinite
square well where the left half of the well rises at a linear rate
to a potential of V0in a time τ, and then falls back at a
linear rate in a time τ. What is the probability that the
particle is now in the first excited state?

quantum physics:
Considera particle in the ground state of an infinite square well
where the left half of the well rises at a linear rate to a
potential of V0in a time t, and then falls back at a linear rate in
a time t. What is the probability that the particle is now in the
first excited state?

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 29 minutes ago

asked 39 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago