Solved: Suppose a particle of mass m is confined to a

Chapter 27, Problem 7SL

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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 \(\lambda = h/mv\)) 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 \(KE = n^2 h^2 /8mL^2\), where n is an integer. (c) Calculate the ground-state energy (n = 1) for an electron confined to a box of width \(0.50 \times 10^{-10}\ m\). (d) What is the ground-state energy, and speed, of a baseball (m = 140 g) in a box 0.65 m wide? (e) An electron confined to a box has a ground-state energy of 22 eV. What is the width of the box? [Hint: See Sections 27-8, 27-13, and 11-12.]