An electron is in a one-dimensional box of length 0.5 nm.The wavelength of the photon emitted as the electron transitions from its first excited state to its ground state is
A)103 nm
B)274 nm
C)365 nm
D)402 nm
E)521 nm

Question

Quizplus · Accepted Answer

The energy levels in a one-dimensional box are given by $E_n = \frac{n^2h^2}{8mL^2}$, where $n$ is the quantum number, $h$ is Planck's constant, $m$ is the mass of the electron, 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 $\Delta E = E_2 - E_1$. This energy difference corresponds to the energy of the emitted photon, which can be calculated using $\Delta E = \frac{hc}{\lambda}$, where $c$ is the speed of light and $\lambda$ is the wavelength of the photon. Solving for $\lambda$ gives the wavelength of the emitted photon. Given the specific values for $h$, $m$, $c$, and $L = 0.5$ nm, the calculation yields a wavelength close to 274 nm.

An Electron Is in a One-Dimensional Box of Length 0