Consider an electron for a hydrogen atom in an excited...

Consider an electron for a hydrogen atom in an excited state. The maximum wavelength of electromagnetic radiation that can completely remove (ionize) the electron from the $\mathrm{H}$ atom is $1460 \mathrm{nm}$. Determine the initial excited state for the electron $(n=?)$

Key Concepts

Quantized Energy Levels in the Hydrogen Atom

Electrons in a hydrogen atom occupy discrete energy levels characterized by quantum numbers. The energy of an electron in a specific level is given by the relation E_n = -13.6 eV/n^2, where n is the principal quantum number. This quantization underpins the entire structure of the hydrogen spectrum and dictates the specific energies required for electronic transitions.

Ionization Energy

Ionization energy is the minimum energy required to remove an electron completely from an atom, effectively moving it from a bound state to a free state (n = infinity). In the context of an excited hydrogen atom, the energy needed for ionization depends on the electron’s initial energy level, with higher initial states requiring less energy to ionize compared to the ground state.

Planck-Einstein Relation

The Planck-Einstein relation connects the energy of a photon to its wavelength through the formula E = hc/?, where h is Planck’s constant and c is the speed of light. This relation is fundamental in understanding how electromagnetic radiation can transfer energy to or from electrons in atomic systems.

Rydberg Formula

The Rydberg formula provides a way to calculate the wavelengths of light associated with electronic transitions in a hydrogen atom. It relates the differences in energy levels to the wavelength of emitted or absorbed radiation and is derived from the quantization of energy levels in the atom.

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