A particle is in the ground state of a one-dimensional box of length 1.0 m.What is the minimum value of its momentum (in kg .m/s)?
A)9.9 * 10-34
B)6.6 * 10-34
C)3.3 * 10-34
D)13 * 10-34
E)cannot be solved unless mass of particle is known.

Question

Quizplus · Accepted Answer

The ground state of a one-dimensional box has a wavefunction that is symmetric about the center of the box. The momentum of the particle is related to the wavelength of the wavefunction by p = h/λ, where h is Planck's constant. For the ground state, the wavelength is twice the length of the box: λ = 2L = 2(1.0 m) = 2.0 m. Therefore, the minimum momentum is p = h/λ = (6.626 x 10^-34 kg m^2/s)/(2.0 m) = 3.313 x 10^-34 kg m/s, which is closest to choice C, 3.3 x 10^-34 kg m/s.

A Particle Is in the Ground State of a One-Dimensional