Consider an electron confined to an infinite well of width 2ao (Bohr radius). Compare its energy...

Consider an electron confined to an infinite well of width 2ao (Bohr radius). Compare its energy in its three lowest energy states to the three lowest energy states of the Bohr model of the hydrogen atom. Repeat for a proton confined to a well of width 2x10-15 m (a nucleus).

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genius_generous answered 5 months ago

Consider an electron confined in a one-dimensional infinite potential well having a width of 0.4 nm....

Consider an electron confined in a one-dimensional infinite potential well having a width of 0.4 nm. (a) Calculate the values of three longest wavelength photons emitted by the electron as it transitions between the energy levels inside the well [3 pts.]. (b) When the electron undergoes a transition from the n = 2 to the n = 1 level, what will be its emitted energy and wavelength [2 pts.]. To which region of the electromagnetic spectrum does this wavelength belong?...

Consider a particle of mass ? in an infinite square well of width ?. Its wave...

Consider a particle of mass ? in an infinite square well of width ?. Its wave function at time t = 0 is a superposition of the third and fourth energy eigenstates as follows: ? (?, 0) = ? 3i?3(?)+ ?4(?) (Find A by normalizing ?(?, 0).) (Find ?(?, ?).) Find energy expectation value, <E> at time ? = 0. You should not need to evaluate any integrals. Is <E> time dependent? Use qualitative reasoning to justify. If you measure...

Estimate the ground state for an electron confined to a potential well of width 0.200 nm...

Estimate the ground state for an electron confined to a potential well of width 0.200 nm and height 100 eV. What is the effective well width of the (infinite) well? (Hint: Consider an iterative approach to approximate the penetration depth ? by initially assuming E?V).

A free electron is trapped in an infinite well of width L. a- Give the Schrödinger...

A free electron is trapped in an infinite well of width L. a- Give the Schrödinger equation which describes the movement of the electron. b- Show that Ψ (?) = ???? (nπx/L ) is a solution of this equation c- Show that ? = √2/L d- What is the average position of the electron e- What is the most likely position if n = 3 f- What is the average kinetic energy for n = 3 g- What is the...

An electron is in the ground state of an infinite square well. The energy of the...

An electron is in the ground state of an infinite square well. The energy of the ground state is E1 = 1.35 eV. (a) What wavelength of electromagnetic radiation would be needed to excite the electron to the n = 4 state? nm (b) What is the width of the square well? nm

A particle of mass m is confined to a finite potential energy well of width L....

A particle of mass m is confined to a finite potential energy well of width L. The equations describing the potential are U=U0 x<0 U=0 0 < x < L U=U0 x > L Take a solution to the time-independent Schrodinger equation of energy E (E < U0) to have the form A exp(-k1 x) + B exp(k1 x) x < 0 C cos(-k2 x) + D sin(k2 x) 0 < x < L F exp(-k3 x) + G exp(k3...

An electron is confined by some potential energy well centered about the origin, and is represented...

An electron is confined by some potential energy well centered about the origin, and is represented by the wave function ψ(x) = Axe−x2/L2, where L = 4.48 nm. The electron's total energy is zero. (a) What is the potential energy (in eV) of the electron at x = 0? eV (b) What is the smallest value of x (in nm) for which the potential energy is zero? nm

Calculate all of the energy levels for an electron in the finite potential well of width...

Calculate all of the energy levels for an electron in the finite potential well of width a) L = 10 Å, b) L = 50 Å, c) L = 100 Å and L = 1000 Å using the actual mass of an electron for the conduction band of the AlGaAs/GaAs/AlGaAs quantum well. Repeat problem using a) the effective mass of an electron in GaAs (electron effective mass meff = 0.067*mass of an electron)

An electron is bound to a finite potential well. (a) If the width of the well...

An electron is bound to a finite potential well. (a) If the width of the well is 4 a.u., determine numerically the minimum depth (in a.u.) such that there are four even states. Give the energies of all states including odd ones to at least 3 digits. (b) Repeat the calculation, but now keep the depth of the well at 1 a.u., determine the minimum width (in a.u.)

1) Find the ground state energies and the Bohr radius for the following: a) Positronium: electron...

1) Find the ground state energies and the Bohr radius for the following: a) Positronium: electron and positron b) Muonium: electron and anti-muon c) Muonic hydrogen: muon and proton d) Deuterium: electron and a nucleus with one proton and one neutron

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