Question

a.A free (i.e. unbound) electron has a kinetic energy of 7.5 eV. What is the angular wavenumber of the travelling wave that describes the solution to Schr ̈odinger’s equation for this particle?

b.A particle of mass 6.64 × 10^-27 kg is confined in an infinite square well of width 2.50 × 10^-11 m. It is observed to have an energy of 3.00 eV. How many nodes does its wavefunction have? (Not including those at the walls of the well.)

c.What is the energy (in eV) of an electron confined to an infinite square well of width 3.00 nm if it is in the quantum state with n = 10?

d.A proton is confined to the x-axis, trapped in the third lowest energy state of a one-dimensional square well. If its energy is 1.5 × 10^-4 eV, what is the width of the well?

e.An electron is confined inside a cubic container with impenetrable walls, each of whose sides has length D = 6.5 nm. The potential energy of the confined electron is always zero and its energy levels are given by E_tot = h²(n_1² + n_2² + n_3²)/8m_eD², where the three quantum numbers may take any integer values. When the electron makes a transition from its third lowest energy level to its lowest energy level, a photon is emitted. What is the frequency associated with this photon?

Answer 1