ATOMIC SPECTRA
High Yield Notes
NOTES
NOTES
ATOMIC SPECTRA
SPECTROSCOPY
Spectroscopy:
It is the branch of physics that deals
The formula to find 1/λ value of
with the study of wavelengths and
any series is:
intensities of electromagnetic
1/ wavelength= Rh (1/p^2 - 1/n^2 )
radiation emitted or absorbed by
Where p is the number of orbits
atoms.
where the electron goes and n is
The energy and frequency decrease the number of orbits from where
down the series from Lyman to the electron jumps.
pfund series and wavelength
increases down the series.
series region p n
UV 2 or higher
LAYMEN SERIES 1
region orbits
visible 3 or higher
BALMER SERIES 2
region orbits
infrared 4 or higher
PASCHEN SERIES 3
region orbits
infrared 5 or higher
BRACKKET SERIES 4
region orbits
far
6 or higher
PFUND SERIES infrared 5
orbits
region
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NOTES BOHR MODEL OF
HYDROGEN ATOM
Bohr's Model of atomic The orbital angular
momentum is equal to an
hydrogen:
integral multiple of h/2πr
Neil Bohr in 1913 formulated a semi- mvr= nh/2πr
classical hydrogen atom model When an electron jumps
based on classical physics and from a higher orbit to a lower
quantum theory orbit, energy in the form of a
It has 3 main postulates: photon is emitted.
energy E = hf
An electron bound in a nucleus
E= En -Ep
can orbit around the nucleus
En is the energy of orbit from
without radiating energy. The
where an electron jumps
energy levels or orbits can be
Ep is the energy of orbit
called discrete stationary states
where
of an atom.
electron comes after
jumping.
Radius of Energy of Velocity of
RRRR quantized orbit electron
Quantised orbits
5.29 x 10-11 m is known Energy could be gained or the velocity of
as the Bohr radius. So, lost only in integral electrons present in the
Bohr's assumption multiples of some first Bohr orbit of
smallest unit of energy, a hydrogen atom=v1(H)=
that the angular
quantum (the smallest 2. 18×10^6 m/s.
momentum is
quantized produces the possible unit of energy).
Energy can be gained or
result that the radii of
lost only in integral
the electron's allowed
multiples of a quantum.
orbits are also
This is the quantization of
quantized.
energy.
r=n2h2/4π2mZe2.
The energy of a single
photon is given by
E = hν = hc/λ.
E = hf, where h is Planck's
constant (6.626 x 10-34 or
4.136 x 10-15 eVs.)
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NOTES As the orbit number increases or as The De Broglie wavelength of
an electron moves away from the the electron in Bohr's orbit of
nucleus, the radius increases and hydrogen atom.
the difference between radii also De Broglie wavelength(λ) = h/mv
increases from 1st orbit up to = 6.63×10^−34 /9.1×10^−31 ×
infinity. 2.18×10^6 = 3.34×10^−10m
Energy level diagram: Limitations of Bohr's
n=∞
atomic model:
-0.38
n=6 -0.54 The Bohr Model is very limited in
n=5 -0.85
terms of size. Poor spectral
n=4
-1.51
predictions are obtained when
n=3
Paschen
-3.40
larger atoms are in question.
n=2
It cannot predict the relative
Balmer
intensities of spectral lines.
Bohr's model of an atom failed
to explain the Zeeman Effect
n=1 -13.60 (effect of magnetic field on the
lyman spectra of atoms).
It also failed to explain the Stark
De broglie wavelenghts effect (the effect of an electric
and hydrogen atom: field on the spectra of atoms).
It violates the Heisenberg
The De Broglie‐Bohr model of Uncertainty Principle.
the hydrogen atom presented It could not explain the spectra
here treats the electron as a obtained from larger atoms.
particle on a ring with wave‐like
properties. De Broglie's Excitation and ionization
hypothesizes that matter has
wave-like properties. The
potential:
consequence of de Broglie's
hypothesis; an integral number The excitation potential is
of wavelengths must fit within the potential to be applied
the circumference of the orbit to an electron in the
The De Broglie wavelength is outermost shell of an atom
defined as follows: to lift it to an excited energy
Lambda = h/mv, where the state.
Greek letter lambda represents The ionization potential is
the wavelength, h is Planck's the minimum potential to
constant, m is the particle's be applied to that electron
mass and v is its velocity. One to bring it outside the atom
could also express mv as the so that the atom is ionized.
particle's momentum
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NOTES X-RAY
Inner shell transition and x- Things needed for x-ray
ray characteristics: production:
An electron from a higher inner The three things needed to create
shell may 'fall' into the vacancy. As x-rays are
a result of this transition, an x-ray a source of electrons,
photon is emitted with an energy a means of accelerating the
corresponding to the difference in electrons to high speeds,
the binding energy of the two and a target for the accelerated
shells. electron to interact with. X-rays
The transition of an inner are produced when the free
electron in heavy metals results electrons cause energy to be
in emissions of visible light. released as they interact with
Atomic electron transition is a the atomic particles in the
change (or jump) of an electron target.
from one energy level to
another within an atom or Summary for x-ray
artificial atom. It appears production:
discontinuous as the electron
A current is passed through the
"jumps" from one quantized
tungsten filament and heats it
energy level to another,
up.
typically in a few nanoseconds
As it is heated up the increased
or less.
energy enables electrons to be
released from the filament
Production of x-rays:
through thermionic emission.
The generation of X-rays occurs
The electrons are attracted
when electrons are accelerated
toward the positively charged
under a potential difference and
anode and hit the tungsten
turned into electromagnetic
target with a maximum energy
radiation. An X-ray tube, with its
determined by the tube
respective components placed in a
potential (voltage).
vacuum, and a generator, make up
As the electrons bombard the
the basic components of X-ray
target they interact via
production.
Bremsstrahlung and
characteristic interactions
which result in the conversion
of energy into heat (99%) and x-
ray photons (1%).
The x-ray photons are released
in a beam with a range of
energies (x-ray spectrum) out of
the window of the tube and
form the basis for x-ray image
formation.
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NOTES Continuous x-ray: Properties of x-ray:
A varying frequency of X-rays is They have a shorter wavelength
emitted continuously due to the of the electromagnetic
retardation of the speed of spectrum.
electrons. The X – rays consist of a Requires high voltage to
continuous range of frequencies up produce X-Rays.
to a maximum frequency fmax or They are used to capture
minimum wavelength λmin. This is human skeleton defects.
called continuous X – rays. They travel in a straight line
and do not carry an electric
The minimum wavelength charge with them.
depends on the anode voltage. They are capable of traveling
Continuous X-rays are created in a vacuum.
when a free moving electron
gets in close enough range of
an atomic nucleus that the two
electromagnetically interact
(remember that electrons have
a negative charge and nuclei
have a positive charge). When
this occurs, the electron will
lose some of its kinetic energy.
The cut-off wavelength of
continuous X-rays corresponds
to the maximum energy of an
electron in an X-ray tube. It is
given by, hc/λ=eV, where V is
accelerating potential.
Bremsstrahlung is the
electromagnetic radiation
emitted in the form of photons
when a charged particle is
decelerated upon striking
against another charged
particle. This radiation gives a
continuous X-ray spectrum.
This is also known as “Braking
Radiation”.
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NOTES
CT SCANNER
The conventional (traditional) CT The number of X-rays that pass
scanner uses a fan-shaped X-ray through the object is inversely
beam, which takes a single slice proportional to the density of the
image per scan and moves to the object.
next slice scan position. The spiral Computer tomography (CT) scans,
(helical) CT scanner uses a DAS in just like X-ray imaging, use
which the fan-shaped X-ray beam photons to create images of
and detector (or multidetector) internal tissues. Photons sit on the
move along a helical path relative electromagnetic spectrum
to the object alongside visible light, radio waves
and microwaves, but have higher
The images are made by converting energy.
electrical energy (moving electrons)
into X-ray photons, passing the
photons through an object, and
then converting the measured
photons back into electrons.
Working of CT Scan:
During a CT scan, the patient lies
on a bed that slowly moves
through the gantry while the x-
ray tube rotates around the
patient, shooting narrow beams
of x-rays through the body.
Instead of film, CT scanners use
special digital x-ray detectors,
which are located directly
CT SCAN IMAGE opposite the x-ray source.
Sc
an
Digital , Analog
The formation
conversion
of a CT image is
a distinct three-
phase process.
scan Image Digital
data Recontruction Image
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NOTES
LASER
A laser is a device that emits light Due to pumping activity, an
through a process of optical electromagnetic field appears
amplification based on the inside the laser cavity at the
stimulated emission of natural frequency of the atoms
electromagnetic radiation. The of the material that fills the
term "laser" originated as an cavity. The waves are reflected
acronym for light amplification by back and forth between the
stimulated emission of radiation. mirrors. The length of the cavity
Laser Action The combination is such that the reflected waves
of spontaneous emission first, reinforce each other. The
and then stimulated emission, electromagnetic waves in
causes the laser to "lase," which phase with each other emerge
means it generates a coherent from the end of the cavity
beam of light at a single having a partially reflective
frequency. mirror. The output is a
continuous beam, or a series of
Characteristics of laser:
Working principle: brief, intense pulses.
The output of a laser is a coherent
electromagnetic field. In a coherent We can separate the
beam of electromagnetic energy, characteristics of the laser
all the waves have the same beam into four major
frequency and phase. categories as:
A basic laser consists of a chamber Superior Monochromatism
known as the cavity which is Superior Directivity
designed to reflect infrared, visible Superior Coherence
or ultraviolet waves so that they High Output
reinforce each other. The cavity Using these characteristics of
can contain either solids, liquids or lasers, they are applied in
gasses. The choice of the cavity various fields such as optical
material determines the communication and defense.
wavelength of the output. Mirrors
are placed at each end of the
cavity. One of the mirrors is totally
reflective, not allowing any of the
energy to pass through them. The
other mirror is partially reflective,
allowing 5% percent of the energy
to pass through them. Through a
process known as pumping,
energy is introduced into the
cavity through an external source.
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NOTES Principle of Laser action:
An atom in an excited state can
be stimulated to return from its
higher state back to its lower
state before its natural time, if
the atom in its excited state is
made to hit by a photon of the
same energy as the emitted
photon. {stimulated emission}.
The incident photon is absorbed
by an atom in the ground state
due to which it is excited.
{induced/stimulated
absorption}
If the number of atoms in the
excited state are more than in
the ground state, then this
inversion is called population
inversion.
A metastable state is a high
energy state in which an atom
can stay for a longer time. Or an
electron can take more time to
dexcite [to return to lower state.
Remember this:
SPONTANEOUS EMISSION: NORMAL POPULATION:
The emission of an electron The number of atoms in the
when an electron jumps from ground state is more than the
an higher energy state to a number of atoms in the excited
lower state, spontaneously state in a normal population.
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NOTES HELIUM NEON LASER
Principle of Laser action: The metastable state
electrons of the helium
The excitation mechanism involves atoms cannot return to
electrons colliding with helium ground state by spontaneous
atoms to produce helium metastable emission. However, they can
atoms, which then transfer their return to ground state by
energy to neon laser levels. transferring their energy to
the lower energy state
Working principle: electrons of the neon atoms.
1. In order to achieve population The energy levels of some of
inversion, we need to supply the excited states of the neon
energy to the gain medium. In atoms are identical to the
helium-neon lasers, we use high- energy levels of metastable
voltage DC as the pump source. A states of the helium atoms
high voltage DC produces When the excited electrons
energetic electrons that travel of the helium atoms collide
through the gas mixture. with the lower energy state
2. The gas mixture in helium-neon electrons of the neon atoms,
lasers is composed mostly of they transfer their energy to
helium atoms. Therefore, helium the neon atoms. As a result,
atoms observe most of the energy the lower energy state
supplied by the high voltage DC. electrons of the neon atoms
3. When the power is switched on, a gain enough energy from the
high voltage of about 10 KV is helium atoms and jump into
applied across the gas mixture. the higher energy states or
This power is enough to excite the metastable states whereas
electrons in the gas mixture. The the excited electrons of the
electrons produced in the process helium atoms will fall into the
of discharge are accelerated ground state. Thus, helium
between the electrodes (cathode atoms help neon atoms in
and anode) through the gas achieving population
mixture. inversion.
4. In the process of flowing through The neon excited electrons
the gas, the energetic electrons continue on to the ground
transfer some of their energy to state through radiative and
the helium atoms in the gas. As a nonradiative transitions. It is
result, the lower energy state important for the continuous
electrons of the helium atoms wave (CW) operation.
gain enough energy and jump
into the excited states or
metastable states.
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NOTES
The light or photons emitted Construction:
from the neon atoms will move The resonating system of the He
back and forth between two Ne laser consists of two concave
mirrors until it stimulates other mirrors, one fully reflector and
excited electrons of the neon other partial reflector. The fully
atoms and causes them silvered mirror will completely
Likewise, millions of ground reflect the light whereas the
state electrons of neon atoms partially silvered mirror will reflect
are excited to the metastable most part of the light but allows
states. The metastable states some part of the light to produce
have a longer lifetime. Therefore, the laser beam.
a large number of electrons will
Uses:
remain in the metastable states
and hence population inversion Helium-neon lasers are used in
is achieved. industries.
After some period, the Helium-neon lasers are used in
metastable states electrons of scientific instruments.
the neon atoms will Helium-neon lasers are used in
spontaneously fall into the next the college laboratories.
lower energy states (E2 and E4)
by releasing photons or red
light. This is called spontaneous
emission.
To emit light, optical gain is
achieved. This process of photon
emission is called the stimulated
emission of radiation.
The light or photons emitted
due to stimulated emission will
escape through the partially
reflecting mirror or output
coupler to produce laser light.
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