Question

A hydrogen atom in an excited state emits a photon of frequency ν = 2.468 x 10¹⁵ s⁻¹. If the electron returns to the ground state, in which level was it before the photon was emitted?

Answer 1

The question involves identifying the original energy level of a hydrogen atom electron before it emits a photon. By calculating the energy of the photon and using the Bohr model of the hydrogen atom, as well as the Rydberg formula, the initial energy level can be determined.

Step-by-step explanation:

The question concerns the determination of the initial energy level of an electron in a hydrogen atom before it emitted a photon of a given frequency. This involves understanding the concept of electron transitions between energy levels in atoms and the emission spectra they produce, which can be calculated using the principles of quantum mechanics and the Bohr model of the hydrogen atom.

First, we need to calculate the energy of the emitted photon using the formula E = hν, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν is the frequency of the photon. Once we have the energy of the photon, we can use the known energy levels of the hydrogen atom to determine which energy level the electron was in before the transition. To do this, we can reference the energy of the ground state of hydrogen and calculate the differences between energy levels using the Rydberg formula for the emission lines.