A sample of hydrogen atoms is irradiated with light with...

A sample of hydrogen atoms is irradiated with light with wavelength 85.5 $\mathrm{nm}$ , and electrons are observed leaving the gas. (a) If each hydrogen atom were initially in its ground level, what would be the maximum kinetic energy in electron volts of these photoelectrons? (b) A few electrons are detected with energies as much as 10.2 eV greater than the maximum kinetic energy calculated in part (a). How can this be?

Key Concepts

Hydrogen Atom Energy Levels

Hydrogen atoms have quantized energy states, with the ground state being the lowest. The energy difference between the ground state and higher excited states (such as the first excited state) is significant and can influence photoionization processes. Electrons that start in an excited state require less energy to be removed, which can result in them being emitted with greater kinetic energy compared to electrons from the ground state.

Excited State Photoionization

This concept describes the situation where atoms that are already in an excited state absorb a photon. Since the electron in an excited state is less tightly bound than one in the ground state, a photon of the same energy can impart a greater excess energy (and hence kinetic energy) to the ejected electron. This explains why some emitted electrons can have kinetic energies greater than expected if all atoms were initially in their ground state.

Photon Energy

This concept refers to the energy carried by a photon, which is inversely proportional to its wavelength. It is calculated using the relation E = hc/?, where h is Planck’s constant and c is the speed of light. Understanding photon energy is crucial in determining whether a photon has enough energy to eject an electron from an atom and, if so, how much kinetic energy the electron will have after photoionization.

Ionization Energy

Ionization energy is the minimum energy required to remove an electron from an atom or ion in its ground state. For hydrogen atoms, this energy is well-defined, and any photon with energy exceeding this value can eject the electron. The difference between the photon energy and the ionization energy gives the maximum kinetic energy of the ejected electron when it is released from an atom in its lowest energy state.

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