What is a line spectrum?

State the photon energy relation in terms of frequency.

State the photon energy relation in terms of wavelength.

A photon has frequency \(5.00\times10^{14}\,\mathrm{Hz}\). Find its energy.

A transition emits a \(2.00\,\mathrm{eV}\) photon. Find its wavelength using \(hc=1240\,\mathrm{eV\,nm}\).

For emission, how are the initial and final atomic energies related to the photon energy?

An atom drops from \(-1.50\,\mathrm{eV}\) to \(-3.40\,\mathrm{eV}\). Find the emitted photon energy.

For the \(1.90\,\mathrm{eV}\) photon, find the wavelength using \(hc=1240\,\mathrm{eV\,nm}\).

Why do atoms absorb only selected photon wavelengths?

An atom has levels \(0\), \(2.0\,\mathrm{eV}\), and \(5.0\,\mathrm{eV}\). List the possible emission photon energies.

Why are emission spectra useful for identifying elements?

A spectral line at \(410\,\mathrm{nm}\) is emitted. Find the photon energy in electronvolts.

An atom absorbs \(3.0\,\mathrm{eV}\) from its ground state and later emits photons of \(1.0\,\mathrm{eV}\) and \(2.0\,\mathrm{eV}\). Explain how this is possible.

How does an absorption spectrum differ from an emission spectrum for the same gas?

Why does a line spectrum support quantized atomic energy rather than arbitrary electron energies?

Derive \(E_i-E_f=hc/\lambda\) for an emitted photon.

Explain why a photon with slightly too little energy is not absorbed by an isolated atom.

A gas shows lines at energies \(1.5\), \(2.0\), and \(3.5\,\mathrm{eV}\). Suggest a simple three-level structure that could produce them.

Why do real spectral lines have finite width rather than exact mathematical zero width?

Connect atomic spectra to the failure of a classical continuous-energy atom.