Calculate the wavelength of the line in the atomic spectrum of hydrogen in which n1=1 and n2=3.

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Calculate the wavelength of the line in the atomic spectrum...

Key Concepts

Hydrogen Atomic Spectrum

The atomic spectrum of hydrogen results from electrons transitioning between discrete energy levels within the atom. When an electron drops from a higher to a lower energy level, it emits a photon, the wavelength of which corresponds to a specific line in the hydrogen spectrum. This phenomenon underpins the analysis of spectral lines in atomic physics.

Bohr Model

The Bohr model describes the atom with electrons moving in fixed orbits or energy levels around the nucleus. Each orbit corresponds to a distinct energy state quantized by the principal quantum number. Transitions between these levels involve absorption or emission of energy, which is manifest as photons of specific wavelengths.

Quantum Numbers

Quantum numbers, particularly the principal quantum number, indicate the energy levels and orbits that an electron can occupy in an atom. Changing the quantum number during a transition directly affects the energy and subsequently the wavelength of the emitted or absorbed photon, making quantum numbers crucial in describing atomic spectra.

Atomic Energy Transitions

Atomic energy transitions involve an electron moving between different energy levels, resulting in a change in the electron’s energy. The energy difference between these levels is either absorbed or emitted in the form of a photon. Understanding these transitions is essential for calculating both the energy change and the corresponding wavelength.

Rydberg Formula

The Rydberg formula establishes a mathematical relationship between the wavelength of emitted or absorbed light and the initial and final quantum numbers of the electron transition in hydrogen. This formula is fundamental for predicting spectral line positions and is widely used in the analysis of hydrogen’s atomic spectrum.

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