July 21, 2012

Physics CH # 18


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.

Explain the spectrum of hydrogen atom.

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.
CLASSIFICATION OF LASER
Lasers are divided into three main classes depending upon their origin.
*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.
 


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.
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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