Physics

Problem

Atom A requires photons of wavelength no longer than

250\,\text{nm}

to be ionized from its ground state, whereas atom B requires photons no longer than

150\,\text{nm}

. Which statement about their binding energies is most accurate? a) Atom A has the larger binding energy because binding energy is directly proportional to threshold wavelength. b) Atoms A and B have identical binding energies because both threshold wavelengths lie in the ultraviolet region. c) Atom B has the larger binding energy because a shorter threshold wavelength corresponds to a higher-energy photon. d) The relative binding energies cannot be determined without knowing the photon intensity that strikes each atom.

Intuitive explanation

The key here is connecting photon wavelength to ionization energy through $E = hc/\lambda$ . A shorter wavelength threshold means a higher-energy photon is needed, which reveals a larger binding energy—the energy holding the electron to the nucleus. Since atom B requires shorter wavelengths (higher photon energy) to ionize, it has a stronger grip on its electron and therefore a greater binding energy than atom A.

Intuitive explanation

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