Review Questions
Q.1 The bohr theory
of hydrogen atom is based upon many assumptions. Do any of these assumption
contradict classical physics?
Ans: The assumption in bohr’s theory that an electron moving
around the nucleus in a certain orbit does not radiate energy is contrary to
the classical physics.
Q.2 Why does the
hydrogen gas produced in laboratory not glow and emit radiations?
Ans: A spectrum is given by the light emitted from an
incandescent gas or vapors. For example electric discharge through a gas or
hydrogen filled discharge tube
Q.3 Why are the
energy levels of the hydrogen atom less than zero?
Ans:The energy levels of hydrogen are negative. This shows
that an electron must do that amount of work to escape from electron or to over
come the binding energy of that orbit.
Q.4 If hydrogen gas
is bombarded by electrons of energy 13.6 eV, would you expected to observe all
the lines of hydrogen spectrum?
Ans:the Hydrogen will get ionized because 13.6 is the energy
of ground state and is equal to the ionization energy. As such no spectral
lines will observed.
Q.5 Hydrogen gas at
room temperature absorbs light of wave length equal to the lines in the Lyman
series but not those of Ballmer series. Explain
Ans: Hydrogen gas at room temperature contains electron in
the ground state so the energy it will absorbed must be equal to the difference
of energy in the first orbit and excited
state .so the radiations are related to the Lyman (n=1)
Q.6 How are X-ray
different from the visible radiations?
Ans: Because They
* Are
Penetrating *Cause ionization in
Gases * Can eject photo electrons from
metals * Produce
fluorescence * Can damage living tissues
Q.7 What property of
X-ray makes them so useful in seeing otherwise invisible internal structures?
Ans:In solids atoms are arranged in a manner. which has
distance in the order of X-rays. Hence crystal is used as transmission grating
to produce diffraction of X rays. This crystallography helps us to locate the
internal structure.
Q.8 Explain the
difference between laser light and incandescent lamp(or bulb).
|
Laser light
|
Incandescent
light
|
|
Highly monochromatic
|
Mixture of several
wavelengths
|
|
Coherent Waves
|
It is not coherent
|
|
It consists of
parallel waves
|
It is emitted in all
directions
|
|
Due to stimulated
emission
|
Due to spontaneous
emission
|
Q.9 Name some applications
of laser.
Ans: 1-Three dimensional images of objects obtained by using
laser in a process called Holography.2- As a surgical tool for welding detached
retina.3- To perform precesion survey and length measurements 4-As potential
energy source for inducing nuclear fusion reaction.5-For telephone
communication along optical fibers.6-For cutting the metals
What are the
basic postulates of Bohr's Atomic Theory?
Introduction
Neil Bohr studied
the spectrum of hydrogen atom. On the basis of his study, he proposed a theory,
which is known as Bohr's Atomic theory.
POSTULATES OF BOHR'S ATOMIC THEORY
The important
Postulates of Bohr's Atomic Theory are as follows:
Angular Momentum
Electrons revolve
only in those orbits for which its orbital angular momentum is an integral
multiple of h/2π, i.e.
L = mvr(n) = nh / 2π
Where,
m = mass of
electron
V = velocity of
electron
r(n) = radius of
nth orbit
n = Principal
quantum number
h = Plank's
Constant
1. Energy
The total energy
of an electron remains constant as long as it remains in the same orbit. i.e.
it does not radiate energy while revolving around the nucleus.
2. Energy Release
When an electron
jumps from a higher orbit having energy 'En' to a lower orbit having energy
'Ep' then energy is released in the form of energy 'hv' i.e.
Eo - Ep = hv = hc
/ λ
Where,
v = Frequency of
Photon
λ = Wavelength of
Photon
c = Speed of
light
h = Plank's
constant
Find out the radius, energy and wave number of hydrogen atom with the help of Bohr's Atomic theory.
HYDROGEN
ATOM
A hydrogen atom is
the simplest of all atoms. It consist of a proton in the nucleus and an
electron revolving around the nucleus.
RADIUS OF HYDROGEN ORBIT
Consider an
electron of charge '-e' revolving in a hydrogen atom around a proton of charge
'+e' with constant speed v.
When the electron
revolves around the nucleus, then two forces balance its motion.
Coulomb's Force =
F = ke² / r² -------- (I)
Centrifugal Force
= F = mv² / r ------- (II)
Comparing eq (I)
and (II)
ke² / r²
= mv² / r
=> ke²
/ mv² = r² / r
=> r = ke² /
mv² -------- (III)
According to
Bohr's theory, angular momentum is an integral multiple of h/2π
mvr = nh / 2π
=> v = nh / 2π
mr
=> 1/v = 2π mr
/ nh
Taking square of
both sides
=> 1/v² = 4π²
m² r² / n²h²
Substituting the
above value in eq (III)
r = Ke² / m = 4π²
m² r² / n²h²
=> r / r² =
4π² m k e² / n²h²
=> 1 / r = 4π²
m k e² / n²h²
=> r = n²h² /
4π²m k e²
We know that,
k = 1 /4π Єo
=> 1 / k = 4π Єo
=> r = n²h² /
4 π² m e² x 4π Єo
=> r = n²h² Єo
/ π e²
The above
equation gives the radius of hydrogen atom.
Radii of Various Orbits
Radius of first
orbit of hydrogen atom is calculated by substituting the following values in
the equation of radius.
n = 1
h = 6.25 x
10(-34) J.sec
m = 9.1 x 10(-31)
kg
k = 9 x 10(9)
Nm²/col²
e = 1.6 x 10(-19)
col
r = (1)² (6.625 x
10(-34)² / 4² (9.1 x 10(-31) (9 x 10(9)) (1.6 x 10-19)²
=> r = 0.53 x
10(-10)m
=> r1 = 0.53
Aº
For other orbits
radius is given by
r2 = (2)² x 0.53
Aº
r3 = (3)² x 0.53
Aº
Similarly,
rn = n² x 0.53 Aº
ENERGY OF HYDROGEN ELECTRON
An electron
revolving in the orbit of hydrogen atom possesses kinetic energy as well as
Potential Energy. Therefore, total energy is given by
E = K.E + P.E
------ (I)
Kinetic Energy
When an electron
revolves in the orbit, then coulomb's force is balanced by centrifugal force
ke²/r² =
mv²/r
=> mv²
= ke²/r
=> 1/2
mv² = ke²/2r
=> K.E
= ke²/2r
Potential Energy
Potential energy
is given by
P.E = F.dr
=> P.E = Ke² /
r² dr
=> P.E = ke² 1
/ r² dr
=> P.E = ke²
|-1/r|
=> P.E = -ke²
[1/r - 1/∞]
=> P.E = -ke²
(1/r - 0)
=> P.E = -ke²
/ r
Total Energy
Substituting the
values of K.E and P.E in eq (I)
E = ke² / 2 - ke²
/ r
=> E = k2² /
2r
Since,
r = n² h²/ 4π² m
k e²
=> E = ke² / 2
4π² m k e² / n² h²
=> |E = 2π² m
k² e² / n² h²|
The above
equation gives the energy of the orbits of hydrogen atom. Negative sign shows
that the electron is bound with the nucleus. When energy of the electron
becomes positive, then electron will leave the nucleus.
SPECTRUM OF HYDROGEN ATOM
When an electron
jumps from a higher orbit to a lower orbit, it radiates energy which appears in
the form of a spectral line. A set of such spectral lines is known as hydrogen
spectrum. Hydrogen spectrum is the simplest one which consists of five series.
1. Layman Series
When an electron jumps from a higher orbit to the first
orbit, Laymen Series (ultra violet region) is obtained.
The wavelength
and wave number of Laymen Series can be calculated by
v = R(H) (1/1² -
1/n²)
Where n = 2, 3,
4, ......
2. Balmer Series
When an electron jumps from a higher orbit to the second
orbit then Balmer Series (visible region) is obtained.
The wavelength
and wave number of Balmer Series can be calculated by
v = R(H) (1/2² -
1/n²)
Where n = 3, 4,
5, ......
3. Paschen Series
When an electron jumps from a higher orbit to the third
orbit then Paschen Series (infra red region) is obtained.
The wavelength
and wave number of Paschen Series can be calculated by
v = R(H) (1/3² -
1/n²)
Where n = 4, 5,
6, ......
4. Bracket Series
When an electron jumps from a higher orbit to the fourth
orbit then Bracket Series (infra red region) is obtained.
The wavelength
and wave number of Bracket Series can be calculated by
v = R(H) (1/4² -
1/n²)
Where n = 5, 6,
7, ......
5. Pfund Series
When an electron jumps from a higher orbit to the fifth
orbit then Pfund Series (infra red region) is obtained.
The wavelength
and wave number of Pfund Series can be calculated by
v = R(H) (1/5² -
1/n²)
Where n = 6, 7,
.....
Write a note on spectra of X-rays. Also write down the properties.
Introduction
X-Rays were
discovered by W.K. Roentgen are also known as Roentgen rays. These rays of
shorter wavelength, ranging from 0.1 nm to i nm. X-rays are produced if heavier
atoms are bombarded by energetic electrons.
PRODUCTION OF X-RAYS
A Filament F and
target T are produced in a vacuum chamber and voltage V is applied across the
ends. Electrons are produced by heating the filament. These electrons are
accelerated towards the metal by applying very high voltage (several thousands
volts). When electrons hit the target, then X-rays are produced. There are two
types of spectra obtained from this experiment.
1. A continuous
spectrum of frequencies or X-rays Brems Strahlung.
2.
Characteristics spectrum or a line spectrum of a limited number of fairly
definite frequencies.
1. Continuous Spectra
When electrons
hit the metal target, a continuous spectrum of frequencies of X-rays is
emitted. The frequencies depend upon the accelerating voltage and are very
nearly independent of the material of target.
Continuous
spectrum is produced when electrons pass close to the atomic nuclei. The are
deflected and slowed down due to which they lose their energy. The energy lost
by decelerating electrons appears in the form of photon in the X-ray range. The
process is represented as
Atoms + e(Fast)
-----> Atom + e(Slow) + hv
2. Characteristic Spectra
In the heavy
atoms, electrons are assumed to be arranged in concentric shells at increasing
distance from the nucleus. The electrons of inner shell are much tightly bound
as compared to the electrons of outer shells. Therefore, a large amount of
energy is required to displace them Consequently photons of larger energy are
emitted when atoms are stabilized. Thus the transition of inner shell electrons
gives rise to high-energy spectra or Characteristic spectra. To obtain
characteristic spectra, target metal of higher atomic number is used.
The process of
emission of characteristic spectra takes place as follows. When a highly
energetic incident electrons knocks an electron from the k-shell, a vacancy
occurs in that shell. This vacancy is filled by the arrival of an electron from
outside the k-shell, emitting excess amount of energy in the form of photon.
If the electrons
jumps only one shell and returns with the emission of X-rays to Y shell, then
X-rays are termed as 'Yα' X-rays. If the electron jumps two shells and returns
with emission of X-rays to suppose 'Y' shell, then X-rays are termed as 'Yβ'
rays and so on, where Y may be K, L, M, ......
PROPERTIES OF X-RAYS
1. X-rays are
highly energetic radiation.
2. X-rays are the
most shortest radiations.
3. X-rays are
electromagnetic radiations that move with the speed of light.
4. X-rays have
high penetrating power.
5. X-rays move in
straight line and produce shadow when an obstacle is placed in front of them.
6. X-rays are not
deflected by electric and magnetic fields.
7. X-rays produce
ionization in gases and eject electrons from certain metals.
8. X-rays produce
fluorescence in many substances.
9. X-rays being
electromagnetic waves can be reflected, refracted, diffracted and polarized
under suitable conditions.
USES OF X-RAYS
1. The major use
of X-rays is in medical and diagnostic treatment.
2. X-rays are
used at customs and security posts.
3. The
diffraction property of X-rays is used to detect arms, explosives.
LASER
INTRODUCTION LASER stands for LIGHT AMPLIFICATION BY STIMULATED
EMISSION OF RADIATION.
Laser is a device used to produce very intense, highly directional, coherent and monochromatic beam of light.
Laser of different power and application can be produced by using different materials.
Laser is a device used to produce very intense, highly directional, coherent and monochromatic beam of light.
Laser of different power and application can be produced by using different materials.
CLASSIFICATION OF LASER
Lasers are divided into three
main classes depending upon their origin.
*Solid Laser
*Liquid Laser
*Gas Laser
*Solid Laser
*Liquid Laser
*Gas Laser
BASIC CONDITIONS TO PRODUCE LASER
*There must be a meta stable
state in the system.
*The system must achieve population inversion.
*The photons emitted must be confined in the system for a time to allow them further stimulated emission.
*The system must achieve population inversion.
*The photons emitted must be confined in the system for a time to allow them further stimulated emission.
PRINCIPLE OF LASER
The principle of laser
production is based on the fact that atoms of a material have a number of
energy levels in which at least one is meta stable state.
Consider a three level atomic system having energies E1, E2 and E3 respectively.
Consider a three level atomic system having energies E1, E2 and E3 respectively.
Let the atoms are at ground
state E1. If photons interact with an atom in ground state, the atom
absorbs the photon and reaches the excited state E3 . We know that
the excited state is an unstable state, therefore, electron must return back to
ground state E1 but such transitions are not allowed and the
electron first reach the state E2. Atoms in the state E3
which has a life time of about 10-8 sec decay spontaneously from
state E3 to state E2 which is meta stable and has life
time of 10-3sec . This means that the atoms reach state E2 much
faster than they leave state E2. This results in an increase in
number of atoms in state E2, and hence population inversion is
achieved.
After achieving population
inversion it is exposed to a beam of photons which causes induced emission of
photons and a beam of laser is produced.
RUBY LASER
CONSTRUCTION
Ruby is a crystal of Al2O3, a
small number of whose Al atoms are replaced by Cr+3 ions. A high intensity
helical flash lamp surrounding the ruby rod is used as light source to raise Cr
atoms from state E1 to E3
The ruby laser is
a cylindrical rod with parallel, flat reflecting ends. One end is partially
reflecting. The flash light is attached with the high voltage.
WORKING
Let the electrons are raised
from ground state E1 to Excited state E3 which has a life time 10-8 sec.
The atoms from the state E3 make transition to state E2. Since E2 is
meta-stable state having life time equal to 10-3 sec. This means
that the atoms reach state E2 much faster than they leave state E2.
This results in an increase in the number of atoms in state E2 and
hence population inversion is achieved.
In this process few Cr atoms
make spontaneous transition from E2 to E1 and emitted photons stimulate further
transition. In this way we obtain an intense, coherent, monochromatic beam of
red laser
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