# Emission Spectrum of the Hydrogen Atom

## The emission spectrum of atomic hydrogen is divided into a number of spectral series.

#### Key Points

• The wavelengths in the spectral series are given by the Rydberg formula.

• These observed spectral lines are due to electrons moving between energy levels in the atom.

• Further series are unnamed, but follow exactly the same pattern as dictated by the Rydberg equation.

#### Terms

• That which is emitted or sent out.

• Specifically, a range of colours representing light (electromagnetic radiation) of contiguous frequencies; hence electromagnetic spectrum, visible spectrum, ultraviolet spectrum, etc.

#### Figures

1. ##### Emission Spectrum of H Atom

Spectral series of hydrogen

2. ##### Electron Transitions and Their resulting Wavelengths for Hydrogen

Three of the transition series in hydrogen. Not to scale.

3. ##### H Emission Series

Standard emission lines and series n the hydrogen atom

4. ##### The line spectrum of hydrogen

Explain how the lines in the emission spectrum of hydrogen are related to electron energy levels. You need to understand convergence, production of UV,vis,IR, excitation, concentric energy levels and be able to draw the line spectra.Dr Atkinson was safely returned to Earth without passing through the intervening space...

The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted by the atom's electrons when they are returned to a lower energy state. Each element's emission spectrum is unique; therefore, spectroscopy can be used to identify the elements in matter of unknown composition. Similarly, the emission spectra of molecules can be used in chemical analysis of substances.

The emission spectrum of atomic hydrogen Figure 4 is divided into a number of spectral series Figure 1, with wavelengths given by the Rydberg formula: $\frac { 1 }{ \lambda_{vac} } =RZ^2( \frac { 1 }{ {n_1 }^{ 2 } } -\frac { 1 }{ { n_2 }^{ 2 } })$,

where R is the Rydberg constant (approximately 1.09737 x 107 m-1), $\lambda_{vac}$ is the wavelength of the light emitted in vacuum, Z is the atomic number, and n1 and n2 are integers such that n1 < n2. These observed spectral lines are due to electrons moving between energy levels in the atom Figure 2. The spectral series are important in astronomy for detecting the presence of hydrogen and calculating red shifts. Further series were discovered as spectroscopy techniques developed.

The spectral lines are grouped into series according to n′. Lines are named sequentially starting from the longest wavelength/lowest frequency of the series, using Greek letters within each series. For example, the 2 → 1 line is called "Lyman-alpha" (Ly-α), while the 7 → 3 line is called "Paschen-delta" (Pa-δ). Some hydrogen spectral lines fall outside these series, such as the 21 cm line; these correspond to much rarer atomic events such as hyperfine transitions. The fine structure also results in single spectral lines appearing as two or more closely grouped thinner lines, due to relativistic corrections. Typically one can only observe these series from pure hydrogen samples in a lab. Many of the lines are very faint and additional lines can be caused by other elements (such as helium if using sunlight, or nitrogen in the air). Lines outside of the visible spectrum typically cannot be seen in observations of sunlight, as the atmosphere absorbs most infra-red and ultraviolet wavelengths.

The collection of series, tabulated and referenced to the transition number, can be seen in Figure 3.

#### Key Term Glossary

atmosphere
a layer of gases that may surround a material body of sufficient mass, such as the earth, and that is held in place by the gravity of the body
##### Appears in these related concepts:
atom
the smallest possible amount of matter that still retains its identity as a chemical element, now known to consist of a nucleus surrounded by electrons
##### Appears in these related concepts:
atomic number
The number, equal to the number of protons in an atom that determines its chemical properties. Symbol: Z
##### Appears in these related concepts:
compound
A substance made from any combination elements.
##### Appears in these related concepts:
constant
Consistently recurring over time; persistent
##### Appears in these related concepts:
electromagnetic
Pertaining to electromagnetism.
##### Appears in these related concepts:
Radiation (quantized as photons) consisting of oscillating electric and magnetic fields oriented perpendicularly to each other, moving through space.
##### Appears in these related concepts:
electron
The subatomic particle having a negative charge and orbiting the nucleus; the flow of electrons in a conductor constitutes electricity.
##### Appears in these related concepts:
element
Any one of the simplest chemical substances that cannot be decomposed in a chemical reaction or by any chemical means, and are made up of atoms all having the same number of protons.
##### Appears in these related concepts:
emission
That which is emitted or sent out.
##### Appears in these related concepts:
energy
a quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent
##### Appears in these related concepts:
frequency
The number of occurrences of a repeating event per unit of time.
##### Appears in these related concepts:
integer
An element of the infinite and numerable set {...,-3,-2,-1,0,1,2,3,...}.
##### Appears in these related concepts:
matter
The basic structural component of the universe. Matter usually has mass and volume.
##### Appears in these related concepts:
molecule
the smallest particle of a specific element or compound that retains the chemical properties of that element or compound; two or more atoms held together by chemical bonds
##### Appears in these related concepts:
nitrogen
a chemical element (symbol N) with an atomic number of 7 and atomic weight of 14.0067
##### Appears in these related concepts:
spectrum
Specifically, a range of colours representing light (electromagnetic radiation) of contiguous frequencies; hence electromagnetic spectrum, visible spectrum, ultraviolet spectrum, etc.
##### Appears in these related concepts:
state
The physical property of matter as solid, liquid, gas or plasma
##### Appears in these related concepts:
substance
Physical matter; material.
##### Appears in these related concepts:
wavelength
the distance between one peak or trough of a travelling oscillation and the next; it is often designated in physics as λ, and corresponds to the velocity divided by the frequency