A proton is in a one-dimensional box of length 2 $\times$ 10^-15 m.Find the wavelength of the photon emitted for a transition between the first excited state and the ground-state. A)8.1 $\times$ 10^-6 nm B)6.1 $\times$ 10^-6 nm C)24 $\times$ 10^-6 nm D)16 $\times$ 10^-6 nm E)12 $\times$ 10^-6 nm

Question

Quizplus · Accepted Answer

The energy levels in a one-dimensional box are quantized and given by the formula $E_n = \frac{n^2h^2}{8mL^2}$, where $n$ is the quantum number, $h$ is Planck's constant, $m$ is the mass of the particle, and $L$ is the length of the box. The energy difference between the first excited state ($n=2$) and the ground state ($n=1$) is used to calculate the wavelength of the emitted photon using the equation $E = \frac{hc}{\lambda}$, where $E$ is the energy difference, $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength. The correct calculation leads to the wavelength of $8.1 \times 10^{-6}$ nm.

A Proton Is in a One-Dimensional Box of Length 2 ×\times×

A Proton Is in a One-Dimensional Box of Length 2 $\times$