Consider an electron in a hydrogen atom. How does the wavelength $\lambda$ of an energy eigen function (as measured around the circular band) depend on the energy $E$ associated with that eigen function?
A) $\lambda \propto|E|$
B) $\lambda \propto \sqrt{|E|}$
C) $\lambda$ is independent of $E$.
D) $\lambda \propto 1 / \sqrt{|E|}$
E) $\lambda \propto 1 /|E|$

Question

Quizplus · Accepted Answer

The wavelength $\lambda$ of an energy eigenfunction in a hydrogen atom is inversely proportional to the square root of the absolute value of the energy $E$, as described by the de Broglie relation, which relates the momentum of a particle to its wavelength. Since the kinetic energy (and thus the total energy in the case of a hydrogen atom, where potential energy is negative and proportional to the kinetic energy) is related to the square of the momentum, $\lambda$ scales as the inverse square root of $E$.

Consider an Electron in a Hydrogen Atom λ\lambdaλ Of an Energy Eigen Function (As Measured Around the Circular

Consider an Electron in a Hydrogen Atom $\lambda$ Of an Energy Eigen Function (As Measured Around the Circular