A photon with a wavelength of 93.8 nm strikes a hydrogen atom, and light is emitted by the atom.

step 1 If light of a certain wavelength is added to an atom, it excites the electrons to a given energy

A photon with a wavelength of 93.8 nm strikes a hydrogen...

A photon with a wavelength of $93.8 \mathrm{nm}$ strikes a hydrogen atom, and light is emitted by the atom. How many emission lines would be observed? At what wavelengths? Explain briefly. (See Figure $7.12 .)$

Key Concepts

Rydberg Formula

The Rydberg formula is a key tool for calculating the wavelengths of the spectral lines produced by electron transitions in hydrogen. It relates the inverse of the wavelength of the emitted or absorbed light to the difference between the inverses of the squares of the initial and final quantum numbers. This formula helps predict both the location and number of lines in the hydrogen emission spectrum.

Electron Transition Cascades and Emission Lines

Once an electron is excited to a higher energy level, it will eventually return to lower levels through a series of transitions, emitting photons at each step. The total number of possible emission lines can be calculated using the formula n(n - 1)/2, where n is the principal quantum number of the highest excited state. This concept explains the cascade of emissions observed after the initial absorption event.

Photon Absorption and Electron Excitation

When a photon strikes a hydrogen atom, it can be absorbed if its energy matches the exact gap between two energy levels, causing the electron to jump from a lower level to a higher (excited) state. This process underpins the excitation mechanism in atoms, setting the stage for subsequent electron transitions and photon emissions.

Hydrogen Atom Energy Levels

In the Bohr model, electrons in a hydrogen atom occupy discrete energy levels characterized by a principal quantum number (n). The energy difference between these levels is quantized, and electron transitions between them result in the absorption or emission of photons with specific energies. This concept is fundamental to understanding the spectral lines observed in atomic emission or absorption spectra.

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