The light emitted from one of the following electronic...

The light emitted from one of the following electronic transitions $(n=4 \longrightarrow n=3$ or $n=3 \longrightarrow n=2)$ in the hydrogen atom causes the photoelectric effect in a particular metal, while light from the other transition does not. Which transition causes the photoelectric effect and why?

The light emitted from one of the following electronic transitions $(n=4 \longrightarrow n=3$ or $n=3 \longrightarrow n=2)$ in the hydrogen atom causes the photoelectric effect in a particular metal, while
light from the other transition does not. Which transition causes the photoelectric effect and why?

Key Concepts

Electron Transition Energy

The energy of the photon emitted during an electron transition in a hydrogen atom is determined by the difference in energy levels as described by the Bohr model. For instance, a transition from n = 3 to n = 2 produces a photon with higher energy (and therefore a higher frequency) than a transition from n = 4 to n = 3. This higher-energy photon is more likely to meet or exceed the work function of a given metal, triggering the photoelectric effect.

Bohr Model of the Hydrogen Atom

The Bohr model explains the hydrogen atom by postulating that electrons exist in discrete energy levels. Transitions between these levels occur when an electron absorbs or emits a photon, with the photon’s energy corresponding exactly to the difference between these levels. This model provides a quantized view of atomic spectra and is fundamental in understanding the energies associated with electron transitions.

Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are emitted from a metal surface when it is exposed to light whose photons have an energy exceeding a specific threshold. This effect demonstrates the particle nature of light and is sensitive not to the light’s intensity but to its frequency, meaning only photons with sufficient energy can overcome the metal's work function.

Work Function and Threshold Frequency

Every metal has a unique work function, which is the minimum energy required to eject an electron from its surface. Associated with this is the threshold frequency; only photons with frequencies equal to or greater than this threshold (and thus energies equal to or greater than the work function) will cause electron emission. Factors influencing the photoelectric effect include whether the light’s energy, determined by its frequency, meets this required level.

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