To excite an electron in a one-dimensional box from its first excited state to its second excited state requires 23.05 eV. What is the width of the box? Give your answer in nm.

Please give a detailed explanation. The answer is 2.

An electron is confined to a one-dimensional region in which its ground-state (n = 1) energy is 1.45 eV. (a) What is the length L of the region? nm(b) What energy input is required to promote the electron to its first excited state? eV

A finite potential well has a potential of 0 between a = 0 and a = L. For an electron, the difference between the ground state and the outside potential is 3 eV. At what distance to the left of the well does the probability density of the electron drop to 0.0001 its value just inside? a. 0.52 nm b. 1.04 nm c. 0.26 nm d. It will never drop to 0.0001 no matter how far you go to the left of the well. e. The probability density is identically zero outside the well. Which statement regarding the well is true? a. The well has infinitely many energy levels. b. For a sufficiently small nonzero outside potential, there won't be any energy levels left. c. No matter how small the nonzero outside potential, there is at least one energy level in the well.

2. An electron is confined to a nanowire 2 nm in length. Model this system as a 1-D particle-in-a-box, going from 0 to 2 nm. a. Compute the probability that the electron is in the range 0.95 ≤ x ≤ 1.05 nm for the states n = 1, 2, 3. b. Compute the probability that the electron is located within a distance of 0.05 nm of the left end of the wire for each of the states n = 1, 10, 100.

The oxygen nucleus 16O has a radius of 3.0 fm.a. With what speed must a proton be fired toward an oxygen nucleus to have a turning point 1.0 fm from the surface?Assume that the nucleus is heavy enough to remain stationary during the collision.b. What is the proton’s kinetic energy in MeV?

a.Draw the wave function for a particle in a box at the n-3 energy level. b.Draw the probability distribution for a particle in a box at the n-3 energy level. c.A nanoparticle with mass equal to 15 x 10-27 g exists in a 10 nm one-dimensional box. What is the wavelength of radiation emitted when it decays from the n-3 level to the n- 2 level? For a 1 nm box?

QUESTION 5 Consider an electron inside the potential well of dimension 8.9 nm wide. The ground state energy of this electron is closest to: a. 0.0056 eV O b. 0.0046 eV C. 0.0066 eV O d. 0.0086 eV

1. a. What is the total number of orbitals associated with the principal quantum number n=1? b. What is the total number of orbitals associated with the principal quantum number n=2? c. What is the total number of orbitals associated with the principal quantum number n=3?| d. What conclusion can be drawn from total number of orbitals associated with a given principal quantum number? 2. List the values of n, {, m, for an orbital in the 4d subshell.

When light of wavelength 310 nm is incident on a metal surface, electrons are ejected with a kinetic energy of 1.0 eV. a. What is the work function (binding energy) of this metal (in eV)? b. What is the cutoff wavelength of light (in nm) that can eject electrons? Will photons with wavelength 544 nm eject electrons? Explain your reasoning. c. Determine the wavelength of light (in nm) that should be used to double the kinetic energy of the electrons ejected from this surface.