If an electron is confined to a one-dimensional box 200 pm in length, calculate the zero-point energy. A) 1.51 * 10^-18 J B) 6.04 * 10^-18 J C) 1.51 * 10^-20 J D) 1.21 * 10^-19 J E) 1.21 * 10^-17 J

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Quizplus · Accepted Answer

The zero-point energy for an electron in a one-dimensional box can be calculated using the formula $E_n = \frac{n^2h^2}{8mL^2}$, where $n=1$ for the ground state (zero-point energy), $h$ is Planck's constant, $m$ is the mass of the electron, and $L$ is the length of the box. Given $L = 200 \, \text{pm} = 200 \times 10^{-12} \, \text{m}$, $h = 6.626 \times 10^{-34} \, \text{Js}$, and $m = 9.109 \times 10^{-31} \, \text{kg}$, substituting these values into the formula gives a zero-point energy value that matches choice A.

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