An excited hydrogen atom with an electron in the n=5 state...

An excited hydrogen atom with an electron in the $n=5$ state emits light having a frequency of $6.90 \times 10^{14} \mathrm{~s}^{-1}$. Determine the principal quantum level for the final state in this electronic transition.

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Key Concepts

Quantized Energy Levels

Electrons in atoms occupy discrete energy levels, which are determined by quantum numbers. This quantization means that electrons can only exist in certain fixed states, and each state has a characteristic energy. Transitions between these levels result in the emission or absorption of energy in the form of photons.

Photon Emission and Energy Conservation

When an electron transitions from a higher energy level to a lower one, it emits a photon with energy equal to the difference between the two levels. This principle, based on the conservation of energy, is key to understanding atomic spectral lines.

Planck's Equation (E = hf)

Planck's equation relates the energy (E) of a photon to its frequency (f) using Planck's constant (h). This fundamental relation connects the quantized nature of energy in atoms with the observable properties of electromagnetic radiation, such as frequency and wavelength.

Rydberg Formula

The Rydberg formula is used to calculate the wavelengths or frequencies of photons emitted or absorbed during electronic transitions in hydrogen-like atoms. It provides a quantitative description of the spectral series and is essential for predicting the outcomes of electron transitions between energy levels.

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