Atomic Spectrum of Hydrogen
Atomic Spectra
❒When an element in the vapour or the gaseous state is heated in a
flame or a discharge tube, the atoms are excited (energised) and emit light
radiations of a characteristic colour. The colour of light produced indicates
the wavelength of the radiation emitted.
❒For example, a
Bunsen burner flame is coloured yellow by sodium salts, red by strontium and violet
by potassium. In a discharge tube, neon glows orange-red, helium-pink, and so
on.
❒If we examine
the emitted light with a Spectroscope (a device in which a beam of light is
passed through a prism and received on a photograph), the spectrum obtained on
the photographic plate is found to consist of bright lines.
❒Such a spectrum
in which each line represents a specific wavelength of radiation emitted by the
atoms is referred to as the Line spectrum or Atomic Emission spectrum of the
element. The emission spectra of some elements are shown in the following figure.
An individual line of these spectra is called a Spectral line.
❒When white
light composed of all visible wavelengths, is passed through the cool vapour of
an element, certain wavelengths may be absorbed. These absorbed wavelengths are
thus found missing in the transmitted light.
❒The spectrum
obtained in this way consists of a series of dark lines which is referred to as
the Atomic Absorption spectrum or simply Absorption spectrum. The wavelengths of
the dark lines are exactly the same as those of bright lines in the emission spectrum.
The absorption spectrum of an element is the reverse of emission spectrum of
the element.
❒Atomic spectral
lines are emitted or absorbed not only in the visible region of the electromagnetic
spectrum but also in the infrared region (IR spectra) or in the ultraviolet
region (UV spectra).
❒Since the
atomic spectra are produced by emission or absorption of energy depending on
the internal structure of the atom, each element has its own characteristic
spectrum.
❒Today spectral analysis
has become a powerful method for the detection of elements even though present
in extremely small amounts.
❒The most
important consequence of the discovery of spectral lines of hydrogen and other
elements was that it led to our present knowledge of atomic structure.
Atomic Spectrum of Hydrogen (Balmer Series)
❒The emission
line spectrum of hydrogen can be obtained by passing electric discharge through
the gas contained in a discharge tube at low pressure.
❒The light
radiation emitted is then examined with the help of a spectroscope. The bright
lines recorded on the photographic plate constitute the atomic spectrum of
hydrogen.
❒In 1884 J.J.
Balmer observed that there were four prominent coloured lines in the visible hydrogen
spectrum:
(1) a red line with a wavelength of 6563 Å.
(2) a blue-green line with a wavelength 4861 Å.
(3) a blue line with a wavelength 4340 Å.
(4) a violet line with a wavelength 4102 Å.
❒The above
series of four lines in the visible spectrum of hydrogen was named as the
Balmer Series. By carefully studying the wavelengths of the observed lines,
Balmer was able empirically to give an equation which related the wavelengths
(λ) of the observed lines.
❒The Balmer
Equation is:
R is a constant called the Rydberg Constant which has the value
109, 677 cm–1 .
n = 3, 4, 5, 6 etc. That is, if we substitute the values of 3, 4, 5
and 6 for n, we get, respectively, the wavelength of the four lines of the
hydrogen spectrum.
❒In addition to
Balmer Series, four other spectral series were discovered in the infrared and ultraviolet
regions of the hydrogen spectrum. These bear the names of the discoverers. Thus
in all we have Five Spectral Series in the atomic spectrum of hydrogen:
❒Balmer equation
had no theoretical basis at all. Nobody had any idea how it worked so accurately
in finding the wavelengths of the spectral lines of hydrogen atom. However, in
1913 Bohr put forward his theory which immediately explained the observed
hydrogen atom spectrum.
Bohr’s Explanation of Hydrogen Spectrum
❒The solitary
electron in hydrogen atom at ordinary temperature resides in the first orbit (n
= 1) and is in the lowest energy state (ground state).
❒When energy is
supplied to hydrogen gas in the discharge tube, the electron moves to higher
energy levels viz., 2, 3, 4, 5, 6, 7, etc., depending on the quantity of energy
absorbed. From these high energy levels, the electron returns by jumps to one
or other lower energy level. In doing so the electron emits the excess energy
as a photon. This gives an excellent explanation of the various spectral series
of hydrogen.
❒Lyman series is
obtained when the electron returns to the ground state i.e., n = 1 from higher energy
levels (n2 = 2, 3, 4, 5, etc.). Similarly, Balmer, Paschen, Brackett
and Pfund series are produced when the electron returns to the second, third,
fourth and fifth energy levels respectively as shown in the following figure:
❒Value of
Rydberg’s constant is the same as in the original empirical Balmer’s equation.
❒According to
equation (1), the energy of the electron in orbit n1 (lower) and n2
(higher) is
The difference of energy between the levels n1 and n2
is :
According to Planck’s equation:
where λ is wavelength of photon and (c) is velocity of light. From
equation (1) and (2), we can write:
where R is Rydberg constant. The value of R can be calculated as
the value of (e, m, h and c) are known. It comes out to be 109,679 cm–1
and agrees closely with the value of Rydberg constant in the original empirical
Balmer’s equation (109,677 cm–1).
Calculation of wavelengths of the spectral lines of
Hydrogen in the visible region:
❒These lines
constitute the Balmer series when n1 = 2. Now the equation (3) above
can be
written as:
❒Thus the
wavelengths of the photons emitted as the electron returns from energy levels
6, 5, 4 and 3 were calculated by Bohr. The calculated values corresponded
exactly to the values of wavelengths of the spectral lines already known. This
was, in fact, a great success of the Bohr atom.
Solved Problem
Find the wavelength in Å of
the line in Balmer series that is associated with drop of the electron from the
fourth orbit. The value of Rydberg constant is 109,676 cm–1.
Solution
The wavelengths of lines in Balmer series are given by:
where λ = wavelength, R (Rydberg constant) = 109,676 cm–1
; n = 4.
Wavelength of the spectral line is 6561 Å
Shortcomings of The Bohr Atom
(1) The great success of the Bohr theory was in its ability to predict
lines in the hydrogen atom spectrum. But it was spectacularly unsuccessful for
every other atom containing more than one electron.
(2) We no longer believe in well-defined electron orbits as was
assumed by Bohr. In fact, in view of modern advances, like dual nature of
matter, uncertainty principle, any mechanical model of the atom stands
rejected.
(3) Bohr’s model of electronic structure could not account for the
ability of atoms to form molecules through chemical bonds. Today we only accept
Bohr’s views regarding quantization as nobody has explained atomic spectra
without numerical quantization and no longer attempted description of atoms on
classical mechanics.
(4) Bohr’s theory could not explain the effect of magnetic field
(Zeeman effect) and electric field (Stark effect) on the spectra of atoms.
Sommerfeld’s Modification of Bohr Atom
❒When spectra
were examined with spectrometers, each line was found to consist of several closely
packed lines. The existence of these multiple spectral lines could not be
explained on the basis of Bohr’s theory.
❒Sommerfeld
modified Bohr’s theory as follows. Bohr considered electron orbits as circular
but Sommerfeld postulated the presence of elliptic orbits also.
❒An ellipse has
a major and minor axis. A circle is a special case of an ellipse with equal
major and minor axis. The angular momentum of an electron moving in an elliptic
orbit is also supposed to be quantized. Thus only a definite set of values is
permissible. It is further assumed that the angular momentum can be an integral
part of (h/2π) units, where h is Planck’s constant. Or that,
❒where (k) is
called the azimuthal quantum number, whereas the quantum number used in Bohr’s theory
is called the principal quantum number. The two quantum numbers n and k are related
by the expression:
❒The values of (k)
for a given value of (n) are k = n – 1, n – 2, n – 3 and so on. A series of
elliptic orbits with different eccentricities result for the different values of
k. When n = k, the orbit will be circular. In other words (k) will have (n)
possible values (n to 1) for a given value of (n). However, calculations based
on wave mechanics have shown that this is incorrect and the Sommerfeld’s modification
of Bohr atom fell through.
Reference: Essentials of Physical Chemistry /Arun Bahl, B.S Bahl and G.D. Tuli / multicolour edition.
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