Download the hydrogen spectrum and shells

ELECTRONS IN ATOMS
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THE HYDROGEN SPECTRUM AND SHELLS
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OBJECTIVES
• Interpreting
emission
spectra
• The Bohr model of the atom
• Quantized energy levels (shells)
• Principal
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quantum
numbers
The Balmer series
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The Balmer series is the most
straightforward
part of the hydrogen
emission spectrum to study because it
occurs in the visible region of the
electromagnetic spectrum. Each line
in the series represents
electromagnetic
radiation of a specific
single wavelength.
(The purple line,
for example, is at 434.05 nm.) The
energy of the radiation may be
calculated by using Planck's equation:
Atoms are far too small for us to see their structure directly. We have to
devise pictures and models that explain the results of experiments we
carry out on them. This process is rather like poking at an elephant with
sticks through the bars of a darkened cage. We then have to use the
evidence gathered on the ends of our sticks to draw the elephant! Our
unknown specimen is not an elephant, but the hydrogen atom. It is
contained inside a discharge tube, and its outer skin is defined by its
surrounding electrons. We poke at it with electrical energy and look at
the electromagnetic radiation that results. We then try to conjure up a
picture of the atom in our minds.
The hydrogen spectrum
An atom of hydrogen consists of just one proton with one surrounding
electron. The emission spectrum of hydrogen is relatively simple
compared to those of other elements. The complete spectrum of
hydrogen consists of separate series of distinct wavelengths concentrated
in the ultraviolet, visible, and infrared regions of the electromagnetic
spectrum. The six series found are named after their discoverers. In
order of increasing wavelength they are the Lyman series (ultraviolet),
Balmer series (visible), Paschen, Brackett, Pfund, and Humphreys series
(infrared). Each of these series is called a line spectrum because the
film-record from the spectrometer appears as a pattern of separate thin
vertical lines.
Shells
Bohr labelled each of the energy levels in the hydrogen atom with a
number called the principal quantum number, n. The energy level
closest to the nucleus is labelled n = 1. The next energy levels are n = 2,
n = 3, and so on. Each of these energy levels is called a shell. The
principal quantum number defines the energy of the electron in a given
shell. In an unexcited hydrogen atom, the electron is in the energy level
n = 1. This state of lowest energy for the atom is called the ground state.
Bohr showed that the series in the high-energy ultraviolet region (the
Lyman series) arises from electronic transitions from higher energy levels
to the energy leveln = 1. Each line in the Lyman series is due to
electrons returning from a particular higher energy level to the energy
leveln = 1. The Balmer series arises from electronic transitions from
higher energy levels to the energy leveln = 2. Each line in the Balmer
series is due to electrons returning from a particular higher energy level
to the energy level n = 2.
n~5---------.---------------------------------------------n~4---------'_---'----------------------------------------
Excitation - transitions
to higher energy levels
Transitions to lower energy
levels emit energy in the form
of electromagnetic
radiation
If an atom collides with another atom,
or absorbs radiation, this can increase
the energy of an electron within the
atom. The electron moves into a higher
energy level. The atom emits
electromagnetic radiation when the
electron moves to a lower energy level.
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Differences
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The Greek capital letter delta i1 is
often used (as here) to describe a
difference between two quantities.
Here i1E is a difference in energy.
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E(radiation) = E(higher) - E(lower) = l'lE
If you combine this equation with Planck's equation, you can see that the
frequency (f) of the radiation emitted depends on the energy level
difference (l'lE) of the particular electronic transition:
l'lE =
hf
So, electronic transitions between energy levels result in emission of
radiation of different frequencies and therefore produce different lines in
the spectrum.
advanced CHEMISTRY
The various series in the low-energy
infrared region are caused by
electrons returning to the energy
levels n = 3 (Paschen series), n = 4
(Brackett series), n = 5 (Pfund series),
and n = 6 (Humphreys series).
The convergence
limit
n~3--r-----~~~--~~r-~~'--B-a-lm--e-r-----------------------------...
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The separate lines in a series become
closer together as their wavelength
decreases, i.e. as their frequency (and
energy) increases. At the highfrequency end of the series, the lines
are so close together that they form a
continuous band of radiation, known
as a continuum.
series
(visible)
E ~ hf
Quantized energy levels
In 1913, Niels Bohr introduced his model of the hydrogen atom. He
assumed that the electron within the hydrogen atom will not absorb or
radiate energy so long as it stays in one of a number of circular orbits.
His model of the atom was designed to explain the observation that the
electromagnetic radiation emitted by an excited hydrogen atom has
specific energies. These energies are fixed, or quantized. Bohr suggested
that the energy of an electron in an atom must also be quantized, so the
electron can only have certain discrete energy levels rather than a
continuous range of possible energies. Each of these energy levels may
be occupied by an electron of the appropriate energy.
When an atom is excited by absorbing energy, an electron jumps up to
a higher energy level. In the Bohr model, the electron is then circling at a
greater distance from the nucleus. The excited atom can emit energy in
the form of electromagnetic radiation as the electron falls back down to
a lower energy level. When an electron moves from one energy level to
another, this is called an electronic transition. The emitted energy can
be seen as a line in the spectrum (as viewed through a spectrometer, for
example). If the electron energy levels were not quantized but could have
any value, a continuous spectrum rather than a line spectrum would
result.
The difference in energy l'lE between the two energy levels in this
electronic transition, E(higher) and E(lower), is equal to the energy of
the emitted radiation, E(radiation):
Series in the infrared
Lyman
series
(UV)
400
500
600
Wavelength
700
/ nm
The start of this continuum, beyond
which separate lines cannot be
distinguished,
is called the
convergence limit. The convergence
limit corresponds to the point at
which the energy of an electron within
the atom is no longer quantized. At
that point, the nucleus has lost all
influence over the electron; the atom
has become ionized.
For the Lyman series, the
convergence limit represents the
ionization
of the hydrogen atom:
H(g) -7 H+(g) + e-(g)
n=.l--~~--~------
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The Lyman series of lines results from electronic transitions from higher energy
levels down to energy level n = 1. The Balmer series results from electronic
transitions down to energy level n = 2.
SUMMARY
• Electrons within atoms occupy fixed energy levels.
• The energy of an electron in an atom is quantized; the electron may
have only certain energies.
• Energy levels with the same principal quantum number are' in the
same shell.
• Atoms emit electromagnetic radiation when electrons move from a
higher to a lower energy level.
PRACTICE
1 Draw an energy level diagram to show the
electronic transitions responsible for the lowestenergy spectral lines in the Paschen series.
2 In no more than 60 words each, explain the
meanings of the following terms:
advanced
CHEMISTRY
a
b
c
d
Quantized
Principal quantum number
Line spectrum
Convergence limit.
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