Calculate the wavelength in nanometers of the shortest wavelength of light emitted by a hydrogen

step 1 In this question, it asks, calculate the wavelength in nanomeres of the shortest wavelengths of

Calculate the wavelength in nanometers of the shortest...

Key Concepts

Unit Conversion (Nanometers)

In practical spectroscopy and various scientific calculations, wavelengths are often expressed in nanometers (nm). Converting from the standard units used in physical equations (meters) to nanometers is essential for comparing calculated wavelengths with experimental data and standard spectroscopic references.

Photon Energy and Wavelength Relationship

The energy of a photon is inversely proportional to its wavelength, as given by the equation E = hc/?, where h is Planck’s constant and c is the speed of light. This relationship is critical when calculating or understanding how high energy (short wavelength) photons are produced during electron transitions.

Rydberg Formula

The Rydberg formula is a fundamental equation in atomic physics that relates the wavenumber (and hence the wavelength) of spectral lines to the electron transitions between energy levels in an atom. It is particularly useful for hydrogen, where it can be used to calculate the wavelengths of emitted or absorbed light during these transitions.

Energy Level Transitions

In an atom, electrons occupy discrete energy levels. When an electron moves from a higher energy level to a lower one, it emits a photon whose energy equals the difference between these levels. The magnitude of this energy difference determines the wavelength of the emitted light, thus explaining why only specific wavelengths are observed.

Hydrogen Atomic Emission Spectrum

The hydrogen atom has a well-defined emission spectrum resulting from the electron transitions between quantized energy levels. The spectrum includes various series, such as the Lyman series where electrons fall to the ground state (n=1). The shortest wavelength in this series corresponds to the transition from an infinitely high energy level down to the ground state, representing the series limit.

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