Determine the ground state energy of a proton in a box of width 1.0 * 10^-9 m. A)2.1 * 10^-4 eV B)2.1 * 10^-3 eV C)2.1 * 10^-2 eV D)2.1 * 10^-1 eV

Question

Quizplus · Accepted Answer

The ground state energy of a particle in a box is given by the equation $E_n = \frac{n^2h^2}{8mL^2}$, where $n$ is the quantum number (1 for ground state), $h$ is Planck's constant, $m$ is the mass of the particle (proton in this case), and $L$ is the width of the box. Given the constants and the width of the box (1.0 x 10^-9 m), the calculation results in an energy value in the order of 10^-4 eV, making option A the correct choice.

Determine the Ground State Energy of a Proton in a Box