Particle in a box: One fairly crude method of determining the size of a molecule is to treat the molecule as an infinite square well (a box) with an electron trapped inside, and to measure the wavelengths of emitted photons. If the photon emitted during the n = 2 to n = 1 transition has wavelength 1940 nm, what is the width of the molecule? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34J ∙ s, m_el = 9.11 × 10^-31 kg) A) 1.33 nm B) 1.12 nm C) 1.21 nm D) 1.45 nm

Question

Quizplus · Accepted Answer

The energy difference between the n = 2 and n = 1 states in an infinite square well is given by $\Delta E = \frac{h^2}{8mL^2}(n_2^2 - n_1^2)$, where $h$ is Planck's constant, $m$ is the mass of the electron, and $L$ is the width of the well. The wavelength of the emitted photon can be related to the energy difference by $\Delta E = \frac{hc}{\lambda}$, where $c$ is the speed of light and $\lambda$ is the wavelength of the photon. Substituting the given values and solving for $L$ yields approximately 1.33 nm.

Particle in a Box: One Fairly Crude Method of Determining