Question
In: Physics
What is the length of a one-dimensional box in which an electron in the n =...
What is the length of a one-dimensional box in which an electron in the n = 1, state has the same energy as a photon with a wavelength of 600 nm? What is the energy of n = 2 and n =3 state? What energy of a photon, if absorbed by the electron could move it from the n = 1 state to the n = 2 state? Write legibly.
Solutions
genius_generous answered 6 months agoRelated Solutions
1. Calculate the probability of locating an electron in a one-dimensional box of length 2.00 nm...
1. Calculate the probability of locating an electron in a
one-dimensional box of length 2.00 nm and nx=4 between 0
and 0.286 nm. The probability is also plotted. You should compare
(qualitatively) your numerical answer to the area under the curve
on the graph that corresponds to the probability.
An electron is confined in a 3.0 nm long one dimensional box. The electron in this...
An electron is confined in a 3.0 nm long one dimensional box.
The electron in this energy state has a wavelength of 1.0 nm.
a) What is the quantum number of this electron?
b) What is the ground state energy of this electron in a box
c) What is the photon wavelength that is emitted in a transition
from the energy level in part a to the first excited state?
Suppose the electron in a hydrogen atom is modeled as an electron in a one-dimensional box...
Suppose the electron in a hydrogen atom is modeled as an
electron in a one-dimensional box of length equal to the Bohr
diameter, 2a0. What would be the ground-state
energy of this "atom"?
______________eV
Consider a particle of mass m confined to a one-dimensional box of length L and in...
Consider a particle of mass m confined to a
one-dimensional box of length L and in a state with normalized
wavefunction. For a partide in a box the energy is given by
En =
n2h2/8mL2
and, because the potential energy is zero, all of this energy is
kinetic. Use this observation and, without evaluating any
integrals, explain why < px2>=
n2h2/4L2
An electron is in a #D quantum box with each side having length a0. a) What...
An electron is in a #D quantum box with each side having length
a0.
a)
What is the largest wavelength of light emitted when the
electron in the box transitions between levels? Consider only
between levels up to the second excited energy level and express
your answer in terms of a0.
b)
What is the smallest wavelength of light emitted when
considering every possible transition?
a one-dimensional box of length 2.7 nm (1) Calculate the wavelength of electromagnetic radiation emitted when...
a one-dimensional box of length 2.7 nm
(1) Calculate the wavelength of electromagnetic radiation
emitted when the photon makes a transition from n = 2 to n = 1.
Answer in units of µm.
(2) Calculate the wavelength of electromagnetic radiation
emitted when the photon makes a transition from n = 3 to n = 2.
Answer in units of µm
(3) Calculate the wavelength of electromagnetic radiation
emitted when the photon makes a transition from n = 3 to...
An electron confined to a one-dimensional box has energy levels given by the equation En=n2h2/8mL2 where...
An electron confined to a one-dimensional box has energy levels
given by the equation
En=n2h2/8mL2
where n is a quantum number with possible values of 1,2,3,…,m is
the mass of the particle, and L is the length of the box.
Part a
Calculate the energies of the n=1,n=2, and n=3 levels for an
electron in a box with a length of 355 pm .
Enter your answers separated by a comma.
Part b
Calculate the wavelength of light required to...
Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions....
Consider a two-dimensional electron gas in a square box of side
L, with periodic boundary conditions.
a) Derive the density of states per unit energy, D(ε).
b) Find the Fermi wavevector, kF, and the Fermi
energy, εF, in terms of the number of electrons N and
the area of the box, A=L2 .
c) Calculate the density of states at the Fermi energy,
D(εF), expressed in terms of N and A. Calculate the heat
capacity, CV.
Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions....
Consider a two-dimensional electron gas in a square box of side
L, with periodic boundary conditions.
a) Derive the density of states per unit energy, D(ε).
b) Find the Fermi wavevector, kF, and the Fermi
energy, εF, in terms of the number of electrons N and
the area of the box, A=L2 .
c) Calculate the density of states at the Fermi energy,
D(εF), expressed in terms of N and A. Calculate the heat
capacity, CV.
*One dimensional infinite potential well - probability at a location An electron moving in a one-...
*One dimensional infinite potential well - probability at a
location
An electron moving in a one- dimensional infinite square well of
width L is trapped in the n = 1 state. Compute the probability of
finding the electron within the "volume" ?x = 0.019 L at 0.55 L to
three decimal places.
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