Suppose a particle of mass m is confined to a
Chapter 8, Problem 63P(choose chapter or problem)
Problem 63P
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 × 10−10m. (d) What is the ground-state energy, and speed, of a baseball (m = 140 g) in a box 0.50 m wide? (e) An electron confined to a box has a ground-state energy of 22 eV. What is the width of the box?
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