*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.

Expert Solution

When an electron moving in a one- dimensional infinite square well of width L (let walls are placed at x=0 &x=L) is trapped in the n^th state, the corresponding wave function for the particle is

for n=1,

the complex conjugate of the corresponding wave function is

The probability of finding the electron within the "volume" ?x = 0.019 L to x=0.55 L is given by

genius_generous answered 2 years 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?...

A particle in an infinite one-dimensional square well is in the ground state with an energy...

A particle in an infinite one-dimensional square well is in the ground state with an energy of 2.23 eV. a) If the particle is an electron, what is the size of the box? b) How much energy must be added to the particle to reach the 3rd excited state (n = 4)? c) If the particle is a proton, what is the size of the box? d) For a proton, how does your answer b) change?

Find the lowest two "threefold degenerate excited states" of the three-dimensional infinite square well potential for...

Find the lowest two "threefold degenerate excited states" of the three-dimensional infinite square well potential for a cubical "box." Express your answers in terms of the three quantum numbers (n1, n2, n3). Express the energy of the two excited degenerate states that you found as a multiple of the ground state (1,1,1) energy. Would these degeneracies be "broken" if the box was not cubical? Explain your answer with an example!

For the infinite square-well potential, find the probability that a particle in its second excited state...

For the infinite square-well potential, find the probability that a particle in its second excited state is in each third of the one-dimensional box: 0?x?L/3 L/3?x?2L/3 2L/3?x?L There's already an answer on the site saying that the wavefunction is equal to ?(2/L)sin(2?x/L). My professor gave us this equation, but also gave us the equation as wavefunction = Asin(kx)+Bcos(kx), for specific use when solving an infinite potential well. How do I know which equation to use and when? Thanks

For the infinite square-well potential, find the probability that a particle in its fifth excited state...

For the infinite square-well potential, find the probability that a particle in its fifth excited state is in each third of the one-dimensional box: ----------------(0 ≤ x ≤ L/3) ----------------(L/3 ≤ x ≤ 2L/3) ------------------(2L/3 ≤ x ≤ L)

An infinite potential well in one dimension for 0 ≤ x ≤ a contains a particle...

An infinite potential well in one dimension for 0 ≤ x ≤ a contains a particle with the wave function ψ = Cx(a − x), where C is the normalization constant. What is the probability wn for the particle to be in the nth eigenstate of the innite potential well? Find approximate numerical values for w1, w2 and w3.

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 in a 3-dimensional infinite square-well potential has ground-state energy 4.3 eV. Calculate the energies...

A particle in a 3-dimensional infinite square-well potential has ground-state energy 4.3 eV. Calculate the energies of the next two levels. Also indicate the degeneracy of the levels.

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...

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.

Question