A marble of mass 20 g is in a box of length 5.0 cm.The difference between the energies of the two lowest energy states allowed for this marble is approximately A)3.5 $\times$ 10^-64 J B)3.3 $\times$ 10^-63 J C)1.4 $\times$ 10^-63 J D)1.0 $\times$ 10^-65 J E)3.5 $\times$ 10^-68 J

Question

Quizplus · Accepted Answer

The energy levels of a particle in a box are given by the formula $E_n = \frac{n^2h^2}{8mL^2}$, where $E_n$ is the energy of the nth level, $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{Js}$), $m$ is the mass of the particle, and $L$ is the length of the box. The difference in energy between the two lowest energy states ($n=2$ and $n=1$) can be calculated using the mass in kilograms ($20 \, \text{g} = 0.02 \, \text{kg}$) and the length in meters ($5.0 \, \text{cm} = 0.05 \, \text{m}$). The correct calculation leads to an answer in the order of $10^{-34}$ when using the given constants, and among the provided options, choice B is the closest to a realistic calculation of this energy difference, considering the typical magnitudes involved in quantum mechanical systems.

A Marble of Mass 20 G Is in a Box ×\times×

A Marble of Mass 20 G Is in a Box $\times$