Consider two identical conducting wires, lying on the x axis and separated by an air gap of thickness L=1nm. The work function of the metal is W=5 eV. (a) Find the probability that the electron will emerge on the other side of the barrier? (b) Find the electric field needed to allow the tunneling probability of 10-5.

For a quantum particle in a scattering state as it interacts a certain potential, the general expressions for the transmission and reflection coefficients are given by T = Jtrans Jinc R = | Jref Jinc (1) where Jinc, Jref, Jtrans are probability currents corresponding to the incident, reflected, and transmitted plane waves, respectively. (a). potential For the particle incident from the left to the symmetric finite square well -Vo; a < x < a, V(x) = 0 ; elsewhere, show that B Ꭲ ; R = A A

The quantum mechanical tunneling process occurs if an electron is incident on a potential barrier of finite width a and finite height Uo. Calculate the transmission probability for this case assuming a barrier width a=1.4 nm and a barrier height Uo=2.6eV assuming that the energy of the electron is E=2.2eV. Give your result in % and round it off to two decimal places, i.e. the nearest hundredths. U(x) Uo 0 < E < Uo E 01 a

At a temperature of 4 K, the heat capacity of silver is 0.0134 J∕mole ⋅ K. The Debye temperature of silver is 225 K. (a) What is the electronic contribution to the heat capacity at 4 K? (b) What are the lattice and electronic contributions and the total heat capacity at 2 K?

If the force constant for a 1-dimensional harmonic oscillator decreases (and all other parameters and properties remain constant), how does the energy gap between n = 3 and n = 4 states change? (A) The energy gap does not change.(B) The energy gap increases.(C) The energy gap decreases.(D) The energy gap change cannot be determined.

Calculate the partition function of a two-level system at 25 °C with an energy gap of 10-2¹ J, assuming: a) Both states are non-degenerate. b) The ground state is non-degenerate, and the excited state is 3-fold degenerate.

Consider a three-dimensional infinite-well modeled as a cube of dimensions L x L x L. The length L is such that the ground state energy of one electron confined to this box is 0.50eV. (a) Write down the four lowest energy states and evaluate their corresponding degeneracy. (b) If 15 (total) electrons are placed in the box, find the Fermi energy of the system. (c) What is the total energy of the 15-electron system? (d) How much energy would be required to lift an electron from Fermi energy of part (b) to the first excited state? Need full detailed answers and explanations to understand the concept.