Question

In a photoelectron spectroscopy experiment, photons with wavelength 130nm cause the ejection of 6s electrons from gold, but photons with wavelength 105nm cause the electrons to be ejected with greater energy. A student claims this is because the photons with wavelength 130nm are higher in energy than photons with wavelength 105nm . Do you agree or disagree with the student's claim? Justify your answer in terms of the energies of the photons.

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Answer 1

I disagree with the student's claim. The energy of a photon is inversely proportional to its wavelength, according to Planck's equation:

E = hc/λ

where E is the energy of the photon, h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon.

Therefore, photons with a shorter wavelength have higher energy than photons with a longer wavelength. In this case, the photons with a wavelength of 105nm have a shorter wavelength than the photons with a wavelength of 130nm, which means they have higher energy.

The fact that the electrons are ejected with greater energy by the photons with a wavelength of 105nm supports this conclusion. This is because the energy of the ejected electron is equal to the energy of the photon minus the energy required to remove the electron from the atom (i.e. the ionization energy). Since the energy of the photon is higher for the 105nm wavelength than for the 130nm wavelength, the electrons ejected by the 105nm photons have higher energy.

Therefore, the student's claim is incorrect. The photons with a wavelength of 105nm are higher in energy than the photons with a wavelength of 130nm.