Atoms - Spectra
Bohr's model of the H (hydrogen) atom correctly predicted the basic hydrogen atom spectrum. When an
electron in an atom absorbs electromagnetic radiation it jumps to a higher orbit (energy level). The
electron cannot be measured to be in-between energy levels - it must be found in one of the energy
levels (n = 1,2,3 ...) or else it must have left the atom altogether in the process of ionisation, leaving
behind a H+ ion (proton). The further the orbit is from the atomic nucleus (the higher the value of n) in
the Bohr model, the higher the energy of the electron. To move out from, say n = 1 to n = 3, the electron
must absorb a packet of energy equal to the energy it must gain to complete the orbital transition (which
is the energy difference between the orbits, or E(n=3) - E (n=1) ). This energy can come from a
photon
of the correct wavelength, since the energy (E) of a photon is given by:
Where v is the frequency of the light (cycles per second or Hz) and h is Planck's constant (about 6.626 x
10^-34 J.s). The energy difference between two energy levels (n2 and n1) is given by:
If the energy of the photon is equal to this energy change then the electron can absorb it and jump-up from its
current energy level, n1, to the higher energy level, n2. In Bohr's model the electron can jump between any two
energy levels in this way. If atoms in an illuminated gas make such a jump, then they absorb the necessary
energy from the illuminating light source, leaving a narrow black band in the spectrum. The spectrum is all the
component wavelengths of the light laid out from red (long wavelength) to blue (short wavelength) and a
spectrum with one or more black bands in it, corresponding to the missing light absorbed by the atomic
electrons is called an absorption spectrum.

If an electron drops or jumps down from a higher energy level (n2) to a lower energy level (n1) then it must lose
energy equivalent in amount to the energy difference between n2 and n1, E(n2) - E(n1), and if this energy is
emitted as a photon of light then an otherwise dark cloud of atomic gas will emit narrow bands of light where
each line corresponds to a jump-down between two energy levels.
Above: The orbits in Bohr's model of the hydrogen atom showing some of the jumps that give rise to absorption
(jumps up) and absorption (jumps down). In particular, light absorbed/emitted corresponds to visible light for the
Balmer series, which involves transitions up from (absorption) or down to (emission) the second orbit (n = 2).
There is no orbit inside n = 1, so this is the closest the electron can be to the nucleus in Bohr's model.

Notice that the orbits are closer together further away from the nucleus at the centre of the atom (black dot)
which is why the higher energy (blue/violet) spectral lines are closer together that the lower energy red-end
lines. The shorter wavelength blue-violet lines correspond to transitions involving a higher energy orbit and a
low energy orbit, so that the energy change E(n2) - E(n1) is greater. The redder lines correspond to smaller
jumps between two lower energy orbits nearer the nucleus.

Within each series the lines are labeled using Greek letters, with alpha corresponding to the lowest energy
transition, which for the Balmer series is the transition between n = 3 and n = 2, which gives rise to the H-alpha
line. This line is particularly prominent in the
Sun's chromosphere, giving the chromosphere it's orange-red
appearance.

The energy-levels or orbits can also be represented as shown below:
Hydrogen atom spectra
Note the difference:

  • Absorption spectra have black lines (gaps) on a bright background, whereas emission spectra have
    bright lines on a black background.

Note the similarities:

  • In both types of spectra the lines are in the same places.
  • In both types of spectra the lines are more closely spaced toward the blue/violet end of the spectrum.

Note that photons with the higher energy have a higher frequency, and since for a photon:
The higher energy, higher frequency photons have a shorter wavelength and so are toward the blue-end of the
spectrum and the lower energy photons are toward the longer wavelength red-end of the spectrum. Bohr's
model accurately predicts the position of the lines, which corresponds to the energy of the electron orbits, for
the hydrogen atom:
The nucleus would be somewhere beneath the bottom n = 1 line in this diagram. If the electron moves past the
n = infinity band, then it leave the atom as it becomes ionised, and it becomes a free electron - joining a
hypothetical continuity where it may possess any energy greater than the ionisation energy (the energy
difference between n = infinity and n = 1).

Atomic hydrogen has the simplest spectrum of all the atoms, since it only has one electron. The Balmer series
involves electron jumps either to the n = 2 shell from higher shells/orbitals (emission spectrum) or from the n = 2
shell to higher shells/orbitals (absorption spectrum). This is the part of the H spectrum in visible light.
The Balmer series is designated by H (Ly is the Lyman series). The first line of the Balmer series is H-alpha,
which corresponds to transitions between n = 2 and n = 3.
Notice that the lines get closer and closer together – the Balmer series converges to a limit at 364.6 nm in the
ultraviolet. In astronomy, the H emission spectrum occurs when gas is irradiated, such as gas surrounding a
shell star, or emission nebulae. The H absorption spectrum occurs, for example, when matter in a star’s
photosphere absorbs radiation emitted by the star – e.g. the Sun has a strong H-alpha line.

Atoms of elements other than hydrogen, also give spectra, though the presence of more than one electron in
these atoms complicates the spectra. In addition to atoms, molecules also produce spectra (though the energy
transitions involved are generally of different types to those found in atoms). The table below summarises the
spectral characteristics of stars, which are grouped into different spectral classes, starting with class M, for the
coolest reddest stars and ending at class O for the hottest ultra-violet blue stars. Each atom, ion or molecule
gives characteristic spectral lines, from which we can identify what substances are present in the atmospheres
of stars.

When an atom absorbs radiation, causing one or more of its electrons to jump up, the atom is said to be in an
excited state. At some future time the electron will lose its excess energy, a process called de-excitation, and
return to its ground state, emitting one or more photons as it does so.

Note that since a higher energy electron is further from the nucleus, an excited atom has a larger radius than a
ground-state atom. Rydberg atoms are atoms in which an electron is excited to a high energy orbit and these
atoms may have diameters as large as 0.01 mm! Atoms get bigger when they are excited, and shrink when they
are de-excited!
Stars - spectral types
One general point to notice is that the cool M-class stars have spectral lines produced by simple molecules
like titanium(II) oxide, TiO in the upper parts of the star's atmosphere. In hotter stars these lines disappear
as the intense heat breaks down molecules into their constituent atoms. Neutral metal atom lines dominate
in K-class stars. Metals are generally easily oxidised, and in hotter stars spectral lines due to metal ions
are formed - starting with those metals most easily ionised, like calcium, Ca, in  G-class stars. In O-class
stars even the inert element He, which is hard to ionise, occurs as He+ ions which give their own
characteristic lines.

Looking directly at the visible discs (
photospheres) of stars absorption spectra can be seen as the
outermost layers of gas selectively absorb certain wavelengths of light from light coming from the lower
layers further in. Looking at more tenuous layers of gas around stars, such as the
chromosphere, yields
emission lines as this gas is radiated by energy from the photosphere, causing atomic electrons to jump
up, and then the atoms later de-excite as the electrons jump down, emitting photons. Shell stars, which are
surrounded by layers of dust also show strong emission lines as the irradiated excited atoms in the
dust-shell de-excite and emit photons to outer space. Emission nebulae are clouds of gas in space that
show emission spectra. Some of these nebulae are regions of active star-birth (like the Eagle's Claw
Nebula) and contain hot young stars that radiate the gas from within, exciting the atoms. What we see is
the light emitted when atoms in the nebula de-excite and emit photons.
Interactive hydrogen atom spectra!
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