Suppose a particle of mass m is confined to a one-dimensional box of width L. According to quantum theory the particle’s wave (with λ = h/mv) is a standing wave with nodes at the edges of the box.
(a) Show the possible modes of vibration on a diagram.
(b) Show that the kinetic energy of the particle has quantized energies given by KE = n2h2/8mL2, where n is an integer.
(c) Calculate the ground-state energy (n = 1) for an electron confined to a box of width 0.50 x 10–10m.
(d) What is the ground-state energy, and speed, of a baseball (m = 140g) in a box 0.50m wide?
(c) An electron confined to a box has a ground-state energy of 22eV. What is the width of the box?