Final answer:
The ground-state energy of an electron in a one-dimensional box can be used to calculate the width of the box using a formula that involves the quantum number, Planck's constant, the energy, and the mass of the electron.
Step-by-step explanation:
In a one-dimensional box, the ground-state energy of an electron is given by the formula:
En = (n2h2)/(8mL2),
where En is the energy, n is the quantum number (ground state is n = 1), h is Planck's constant, m is the mass of the electron, and L is the width of the box.
To find the width of the box, we can rearrange the formula as:
L = (√(n2h2))/(√(8Em)),
where E is the ground-state energy (2.40 eV) and m is the mass of the electron. Plugging in the values, we find that the width of the box is approximately 0.1422 nm.