What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its energy is 2 h²/mL²? A) 2 B) 8 C) 4 D) 1 E) 16

Question

Quizplus · Accepted Answer

For a particle in a one-dimensional box, the energy levels are given by:
$E_{n}=\frac{n^{2}h^{2}}{8mL^{2}}$
Setting this equal to the given energy:
$\frac{n^{2}h^{2}}{8mL^{2}}=\frac{2h^{2}}{mL^{2}}$
Simplifying:
$n^{2}=16$
Taking the positive square root since n must be positive:
$n=4$
Therefore, the answer is choice C.

What Is the Quantum Number N of a Particle of Mass