Question

In: Physics

An electron is trapped in an infinitely deep one-dimensional well of width 0.288 nm. Initially the...

An electron is trapped in an infinitely deep one-dimensional well of width 0.288 nm. Initially the electron occupies the n = 4 state. (a) Suppose the electron jumps to the ground state with the accompanying emission of a photon. What is the energy of the photon? eV (b) Find the energies of other photons that might be emitted if the electron takes other paths between the n = 4 state and the ground state. 4 → 3 in eV 4 → 2 in eV 3 → 2 in eV 3 → 1 in eV 2 → 1 in eV

Solutions

Expert Solution


Related Solutions

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?...
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 trapped in a square well of unknown width, L. It starts in unknown...
An electron is trapped in a square well of unknown width, L. It starts in unknown energy level, n. When it falls to level n-1 it emits a photon of wavelength λphoton = 2280 nm. When it falls from n-1 to n-2, it emits a photon of wavelength λphoton = 3192 nm. 1) What is the energy of the n to n-1 photon in eV? En to n-1 = 2) What is the energy of the n-1 to n-2 photon...
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?
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).
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.)
*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.
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 trapped in a two-dimensional region of ?? =??= 1.00x10-10 m (a typical atomic...
An electron is trapped in a two-dimensional region of ?? =??= 1.00x10-10 m (a typical atomic diameter). a. Find the energies of the ground state and first two excited states. b. How much energy must be supplied to excite the electron from the ground state to the second excited state? c. From the second excited state, the electron drops down to the first excited state. How much energy is released in this process?
A symmetric GaAs/AlAs RTD has a barrier width of 1.5 nm and a well width of...
A symmetric GaAs/AlAs RTD has a barrier width of 1.5 nm and a well width of 3.39 nm. When this RTD is inserted in the base of an HBT with an emitter flux centered on the first excited level of the RTD. Find the cutoff frequency of the HBT with the inserted RTD, if the original fT was 100GHz. [Hint:The transit time across the RT structure is given by (d/vG) + (2h/Γ)where d is the width of the RT structure,...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT