If an electron is confined to a one-dimensional box 200 pm in length,calculate the zero-point energy.

Question

Quizplus · Accepted Answer

The zero-point energy for a particle confined to a one-dimensional box is given by:
E_0 = (h^2)/(8mL^2)
where h is the Planck constant, m is the mass of the particle, and L is the length of the box.
Given: L = 200 pm = 2x10^-10 m
The mass of an electron is m = 9.10938356×10^-31 kg.
Substituting these values into the above equation, we get:
E_0 = (6.62607015 × 10^-34 J s)^2 / (8 * 9.10938356×10^-31 kg * (2x10^-10 m)^2)
E_0 = 1.51 x 10^-18 J 
Converting to electron volts, we get:
E_0 = 1.51 x 10^-18 J / 1.60218 x 10^-19 J/eV = 9.42 eV
Therefore, the best choice is A.

If an Electron Is Confined to a One-Dimensional Box 200