Atomic Spectra
All condensed matter (solids, liquids, and dense gases) emit
electromagnetic radiation at all temperatures. Also, this radiation has a
continuous distribution of several wavelengths with different
intensities. This is caused by oscillating atoms and molecules and their
interaction with the neighbours. In the early nineteenth century, it was
established that each element is associated with a characteristic
spectrum of radiation, known as Atomic Spectra. Hence, this suggests
an intimate relationship between the internal structure of an atom and
the spectrum emitted by it.
Atomic Spectra
When an atomic gas or vapour is excited under low pressure by
passing an electric current through it, the spectrum of the emitted
radiation has specific wavelengths. It is important to note that, such a
spectrum consists of bright lines on a dark background. This is an
emission line spectrum. Here is an emission line spectrum of hydrogen
gas:
The emission line spectra work as a ‘fingerprint’ for identification of
the gas. Also, on passing a white light through the gas, the transmitted
light shows some dark lines in the spectrum. These lines correspond to
those wavelengths that are found in the emission line spectra of the
gas. This is the absorption spectrum of the material of the gas.
Spectral Series of Atomic Spectra
Normally, one would expect to find a regular pattern in the
frequencies of light emitted by a particular element. Let’s look at
hydrogen as an example. Interestingly, at the first glance, it is difficult
to find any regularity or order in the atomic spectra. However, on
close observation, it can be seen that the spacing between lines within
certain sets decreases in a regular manner. Each of these sets is a
spectral series.
Five spectral series identified in hydrogen are
1. Balmer Series
2. Lyman Series
3. Paschen Series
4. Brackett Series
5. Pfund Series
Further, let’s look at the Balmer series in detail.
Balmer Series
In 1885, when Johann Balmer observed a spectral series in the visible
spectrum of hydrogen, he made the following observations:
● The longest wavelength is 656.3 nm
● The second longest wavelength is 486.1 nm
● And the third is 434.1 nm
● Also, as the wavelength decreases the lines appear closer
together and weak in intensity
● He found a simple formula for the observed wavelengths:
Further, for n=∞, you can get the limit of the series at a wavelength of
364.6 nm. Also, you can’t see any lines beyond this; only a faint
continuous spectrum.Furthermore, like the Balmer’s formula, here are
the formulae for the other series:
Lyman Series
Paschen Series
Brackett Series
Pfund Series
Solved Examples for You
Question: The emission line spectra works as a ______________ for
identification of the gas.
A. clue
B. fingerprint
C. deterrent
D. confuser
Solution: Fingerprint
Question: Name the five spectral series identified in hydrogen gas?
Solution: Balmer series, Lyman series, Paschen series, Brackett series
and Pfund series.
Alpha-Particle Scattering and Rutherford’s Nuclear Model of Atom
In 1911, Rutherford, along with his assistants, H. Geiger and E.
Marsden, performed the Alpha Particle scattering experiment, which
led to the birth of the ‘nuclear model of an atom’ – a major step
towards how we see the atom today.
J.J Thomson’s Plum-pudding Model
In 1897-98, the first model of an atom was proposed by J.J. Thomson.
Famously known as the Plum-pudding model or the watermelon
model, he proposed that an atom is made up of a positively charged
ball with electrons embedded in it. Further, the negative and positive
charges were equal in number, making the atom electrically neutral.
Figure 1 shows what Thomson’s plum-pudding model of an atom
looked like. Ernest Rutherford, a former research student working
with J.J. Thomson, proposed an experiment of scattering of alpha
particles by atoms to understand the structure of an atom.
Rutherford, along with his assistants – H. Geiger and E. Marsden –
started performing experiments to study the structure of an atom. In
1911, they performed the Alpha particle scattering experiment, which
led to the birth of the ‘nuclear model of an atom’ – a major step
towards how we see the atom today.
Figure 1. Source: Wikipedia
The Alpha Particle Scattering Experiment
They took a thin gold foil having a thickness of 2.1×10-7 m and placed
it in the centre of a rotatable detector made of zinc sulfide and a
microscope. Then, they directed a beam of 5.5MeV alpha particles
emitted from a radioactive source at the foil. Lead bricks collimated
these alpha particles as they passed through them.
After hitting the foil, the scattering of these alpha particles could be
studied by the brief flashes on the screen. Rutherford and his team
expected to learn more about the structure of the atom from the results
of this experiment.
Source: Wikipedia
Observations
Here is what they found:
● Most of the alpha particles passed through the foil without
suffering any collisions
● Around 0.14% of the incident alpha particles scattered by more
than 1o
● Around 1 in 8000 alpha particles deflected by more than 90o
These observations led to many arguments and conclusions which laid
down the structure of the nuclear model on an atom.
Conclusions and arguments
The results of this experiment were not in sync with the plum-pudding
model of the atom as suggested by Thomson. Rutherford concluded
that since alpha particles are positively charged, for them to be
deflected back, they needed a large repelling force. He further argued
that for this to happen, the positive charge of the atom needs to be
concentrated in the centre, unlike scattered in the earlier accepted
model.
Hence, when the incident alpha particle came very close to the
positive mass in the centre of the atom, it would repel leading to a
deflection. On the other hand, if it passes through at a fair distance
from this mass, then there would be no deflection and it would simply
pass through.
He then suggested the ‘nuclear model of an atom’ wherein the entire
positive charge and most of the mass of the atom is concentrated in the
nucleus. Also, the electrons are moving in orbits around the nucleus
akin to the planets and the sun. Further, Rutherford also concluded
from his experiments that the size of the nucleus is between 10-15 and
10-14 m.
According to Kinetic theory, the size of an atom is around 10-10 m or
around 10,000 to 100,000 times the size of the nucleus proposed by
Rutherford. Hence, the distance of the electrons from the nucleus
should be around 10,000 to 100,000 times the size of the nucleus.
This eventually implies that most of the atom is empty space and
explains why most alpha particles went right through the foil. And,
these particles are deflected or scattered through a large angle on
coming close to the nucleus. Also, the electrons having negligible
mass, do not affect the trajectory of these incident alpha particles.
Alpha Particle Trajectory
The trajectory traced by an alpha particle depends on the impact
parameter of the collision. The impact parameter is simply the
perpendicular distance of each alpha particle from the centre of the
nucleus. Since in a beam all alpha particles have the same kinetic
energy, the scattering of these particles depends solely on the impact
parameter.
Hence, the particles with a small impact parameter or the particles
closer to the nucleus, experience large angle of scattering. On the
other hand, those with a large impact parameter suffer no deflection or
scattering at all. Finally, those particles having ~zero impact
parameter or a head-on collision with the nucleus rebound back.
Coming to the experiment, Rutherford and his team observed that a
really small fraction of the incident alpha particles was rebounding
back. Hence, only a small number of particles were colliding head-on
with the nucleus. This, subsequently, led them to believe that the mass
of the atom is concentrated in a very small volume.
Electron Orbits
In a nutshell, Rutherford’s nuclear model of the atom describes it as:
● An electrically neutral sphere with
○ A small and positively charged nucleus at the centre
○ Surrounded by revolving electrons in their
dynamically stable orbits
The centripetal force that keeps the electrons in their orbits is an
outcome of:
● The electrostatic force of attraction between-
○ The positively charged nucleus and
○ The negatively charged revolving electrons.
Solved Example for You
Question: Rutherford, Geiger and Marsden, directed a beam of alpha
particles on a foil of which metal
A. Platinum
B. Tungsten
C. Gold
D. Silver
Solution: Gold
Bohr Model of the Hydrogen Atom
Bohr Model of the hydrogen atom attempts to plug in certain gaps as
suggested by Rutherford’s model by including ideas from the newly
developing Quantum hypothesis. Bohr postulated that in an atom,
electrons could revolve in stable orbits without emitting radiant
energy.
Bohr Model
Bohr model of the hydrogen atom attempts to plug in certain gaps as
suggested by Rutherford’s model by including ideas from the newly
developing Quantum hypothesis. According to Rutherford’s model, an
atom has a central nucleus and electron/s revolve around it like the
sun-planet system.
However, the fundamental difference between the two is that, while
the planetary system is held in place by the gravitational force, the
nucleus-electron system interacts by Coulomb’s Law of Force. This is
because the nucleus and electrons are charged particles. Also, an
object moving in a circle undergoes constant acceleration due to the
centripetal force.
Further, electromagnetic theory teaches us that an accelerating
charged particle emits radiation in the form of electromagnetic waves.
Therefore, the energy of such an electron should constantly decrease
and the electron should collapse into the nucleus. This would make the
atom unstable.
The classical electromagnetic theory also states that the frequency of
the electromagnetic waves emitted by an accelerating electron is equal
to the frequency of revolution. This would mean that, as the electron
spirals inwards, it would emit electromagnetic waves of changing
frequencies. In other words, it would emit a continuous spectrum.
However, actual observation tells us that the electron emits a line
spectrum.
Watch Modern Atomic Theory –
Bohr Model Postulates
Bohr, in an attempt to understand the structure of an atom better,
combined classical theory with the early quantum concepts and gave
his theory in three postulates:
Postulate I
In a radical departure from the established principles of classical
mechanics and electromagnetism, Bohr postulated that in an atom,
electron/s could revolve in stable orbits without emitting radiant
energy. Further, he stated that each atom can exist in certain stable
states. Also, each state has a definite total energy. These are stationary
states of the atom.
Postulate II
Bohr defined these stable orbits in his second postulate. According to
this postulate:
● An electron revolves around the nucleus in orbits
● The angular momentum of revolution is an integral multiple of
h/2p – where hàPlanck’s constant [h = 6.6 x 10-34 J-s].
● Hence, the angular momentum (L) of the orbiting electron is: L
= nh/2p
Postulate III
In this postulate, Bohr incorporated early quantum concepts into the
atomic theory. According to this postulate, an electron can transition
from a non-radiating orbit to another of a lower energy level. In doing
so, a photon is emitted whose energy is equal to the energy difference
between the two states. Hence, the frequency of the emitted photon is:
hv = Ei – Ef
(Ei is the energy of the initial state and Ef is the energy of the final
state. Also, Ei > Ef).
Some important equations
Radii of Bohr’s stationary orbits
● n – integer
● rn – radius of the nth orbit
● h – Planck’s constant
● ε0 – Electric constant
● m – Mass of the electron
● Z – the Atomic number of the atom
● e – Elementary charge
Since ε0, h, m, e, and p are constants and for a hydrogen atom, Z = 1,
rn α n2
The velocity of Electron in Bohr’s Stationary Orbits
Since ε0, h, and e are constants and for a hydrogen atom, Z = 1, rn α
(1/n)
Total Energy of Electron in Bohr’s Stationary Orbits
The negative sign means that the electron is bound to the nucleus.
Although these equations were derived under the assumption that
electron orbits are circular, subsequent experiments conducted by
Arnold Sommerfeld reaffirm the fact that the equations hold true even
for elliptical orbits.
Energy Levels
When the electron is revolving in an orbit closest to the nucleus, the
energy of the atom is the least or has the largest negative value. In
other words, n = 1. For higher values of n, the energy is progressively
larger.
The state of the atom wherein the electron is revolving in the orbit of
smallest Bohr radius (a0) is the ‘Ground State’. In this state, the atom
has the lowest energy. The energy in this state is:
E1 = -13.6 eV
Hence, the minimum energy required to free an electron from the
ground state of an atom is 13.6 eV. This energy is the ‘Ionization
Energy’ of the hydrogen atom. This value agrees with the
experimental value of ionization energy too.
Now, a hydrogen atom is usually in ‘Ground State’ at room
temperature. The atom might receive energy from processes like
electron collision and acquire enough energy to raise the electron to
higher energy states or orbits. This is an ‘excited’ state of the atom.
Therefore, the energy required by the atom to excite an electron to the
first excited state is:
E2 – E1 = -3.40 eV – (-13.6) eV = 10.2 eV
Similarly, to excite the electron to the second excited state, the energy
needed is:
E3 – E1 = -1.51 eV – (-13.6) eV = 12.09 eV
Remember, that the electron can jump to a lower energy state by
emitting a photon. Also, note that, as the excitation of the hydrogen
atom increases, the minimum energy required to free the electron
decreases.
Solved Examples for You
Question: How many postulates are present in the Bohr model of a
hydrogen atom?
Solution: Bohr model of a hydrogen atom has three postulates. The
postulate of the circular orbit, postulate of the selected orbit and
postulate of the origin of spectral lines.
Question: According to the Bohr model, what is the energy of the
atom in the ground state?
Solution: According to the Bohr model, the energy of the atom in the
ground state is -13.6 eV.
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