X-ray (FULL EXPLANATIONS)

X-RAY

X – Rays are electromagnetic waves of short wavelength in the range of 10A° to 0.5

The discovery of X – rays goes to 1895 when W. Roentgen discovered while working with a discharge tube. He found that when the pressure in the discharge tube was reduced to about 10-3mm of Hg and the electric discharge was passed between the cathode and anode, the glass wall of the discharge tube behind the cathode began to glow with greenish yellow color. He also observed that a surface coated with barium platinum cyanide placed outside the discharge tube emitted light even when it was shielded from direct visible and ultraviolet light emitted by the discharge tube. After performing a series of experiment, Roentgen concluded that highly penetrating radiation of unknown nature are produced when a beam of fast moving electrons strikes a solid target such as tungsten. He named these radiations X – rays which led to the discovery of X – rays. Diagram of X – ray tube is:

Fig:

Different between X-ray and Ordinary light:

Ordinary light	x-ray
These are visible	These are invisible
They have heating effect	They have no heating effect
The wavelength of ordinary light range from 4 x 10-7m to 7.6 x 10-7m.	The wavelength of x-ray range from 10-9m to 10-12m.
It does not have high penetrating power. Ordinary light penetrates only transparent substance not opaque.	They have high penetrating power and power of transparency for opaque substance

The important properties of X – rays are:

(i) The X – rays are the electromagnetic wave of wavelength 10A° to 0.5°

(ii) The X – ray travels in vacuum with the speed of light ie. 3 * 108m/s.

(iii) They affect high penetrating power.

(iv) They have photographic effect.

(v) They are not deflected by electric and magnetic field.

X-rays are produced by the two methods

a. When fast moving electron having sufficient energy strikes the metal surface of high atomic number,it knock out the some electron from the inner orbit of the target metal due to vacancies are created so, to fill the vacant space electron from the higher energy level jump into these spaces emitting the radiation whose energy is equal to the difference in the energy of two orbits .thus obtained radiations by the heavy metals are X –rays.

b. When the fast moving electron strike the target they are heavily retarded by the coulomb repulsive force due to the charges of the electron of the atom .As a result retarding energy emits the radiation called X-rays.

Bragg’s law:

 Statement: when a monochromatic X-rays impinge upon the atom in the crystal lattice, each atom acts as source of scattering radiation of the same wavelength. The crystal acts as a series of parallel reflecting plane. Then the intensity of the reflected beam at certain angle will be maximum when the path difference between two reflected waves from two different planes is an integral multiple of λ

Explanation of law:

Let us consider a set of parallel plane of atom point at a spacing d between the successive plates. Let a narrow monochromatic X-ray beam of wavelength λ be incident on the first plane at a glance angle ɵ consider the ray PQ incident on the first plane. The corresponding reflected ray QR must be also be incident at the same angle ɵ to the plane. Since X-ray are must more penetrating then that of ordinary light there is only partial reflected at each plane The complete absorption take place only after penetrating several layers. Consider two parallel rays PQR and P’Q’R’ in the beam which reflected by two atom Q and Q’. is vertically below Q. the ray P’Q’R’ has longer path than the ray PQR, To compute the path difference between the two rays from Q draw normal QT and QS on P’Q’ and Q’R’ respectively. Then the path difference =TQ’ +Q’S=d sinɵ +d sinɵ= 2dsinɵ

Hence the two ray will reinforce each other and produce maximum intensity, if

2dsinɵ=nλ where n=1, 2, 3, 4,……………

The integer n gives the order of the scattered beam; λ is the length of X-ray used. This equation is called bragg’s law

It is originated when the fast moving electron strike the target, they are heavily retarded. As the electrons go on being retorted continuously, the frequency of radiation emitted also goes on changing continuously. Hence, continuous X-rays are obtained.

The characteristics spectrum of X – rays origin is explained using Bohr’s postulate i.e. when an electron jumps from higher shell to lower, it emits energy in the form of radiation. So, when the fast moving electron strikes a metal target having high atomic number the electrons can knock out electrons from the inner shells of the atom, thus creating vacant spaces for its origination.

 Some of the features of continuous spectrum of X – rays are:

(i) It consists of all possible wave length within a range.

(ii) The value of maximum intensity increases as potential increases.

Some of the features of characteristics X – ray are:

(i) The line of characteristics X – ray spectra occurs in various groups.

(ii) For each target material, there is minimum potential below which there is no radiation.

Production of X-rays:

X-rays are produce when fast moving electron are suddenly stopped by a solid target. A Coolidge tube is shown in figure.

Figure:

The tube is exhausted to the beast possible vacuum of the order of 10-5mm of Hg. The cathode consist of a tungsten filament (F) heated by a low tension battery. Thermionic electrons emitted by the filament are accelerated toward the target (T) by high P.D. maintained between F and T. the filament is placed inside a metal cup G to focus the electrons on the target. The target must be cooled to remove the heat generated in it by continuous electron- bombardment. The usual method is to mount the target material on a hollow copper tube through which cold water is continuously circulated. The target is made of material like tungsten or molybdenum having a high m.p. and high atomic no. metal with atomic no. give more energetic and intense X-rays when used as target. In the Coolidge tube the intensity and frequency of x-ray can be easily controlled.

The intensity of X-ray is depending upon the no. of electrons striking the target per second. The no. of the electrons give out by filament is directly propatational to its temperature, which can adjust by varying the current in the filament circuit. Therefore the intensity of X-ray varies with the filament current.

The frequency of X-ray emitted depends on the voltage between cathode and anode .let V be the accelerating potential across the tube. If e be the charge on the the electron the the work done on the electron in moving from cathode to anticathode is eV. Then the electron thus gain K.E. which is converted into x-ray when the electron strikes the target.

If υmaxbe the maximum frequencies of the x-ray produce

Then h υmax=eV

or, hC/λmin=eV

or, λmin=hC/eV  where C= velocity of light and h= plank’s constant .

Crystal diffraction

Let us consider a set of parallel plane of atom point at a spacing d between the successive plates. Let a narrow monochromatic X-ray beam of wavelength λ be incident on the first plane at a glance angle ɵ .consider the ray PQ incident on the first plane. The corresponding reflected ray QR must be also be incident at the same angle ɵ to the plane. Since X-ray are must more penetrating then that of ordinary light there is only partial reflected at each plane, The complete absorption take place only after penetrating several layers. Consider two parallel rays PQR and P’Q’R’ in the beam which reflected by two atom Q and Q’. is vertically below Q. the ray P’Q’R’ has longer path than the ray PQR, To compute the path difference between the two rays from Q draw normal QT and QS on P’Q’ and Q’R’ respectively. Then the path difference =TQ’ +Q’S=d sinɵ +d sinɵ = 2dsinɵ

Hence the two ray will reinforce each other and produce maximum intensity, if

2dsinɵ=nλ where n=1, 2, 3, 4,

The integer n gives the order of the scattered beam; λ is the length of X-ray used. This equation is called Bragg’s law.

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Short description of speed of light

                               Speed of light

Wave optics is the branch of opticswhich deals with interference, diffraction, polarization, and other phenomena of light.

Electromagnetic spectrum

 Electromagnetic spectrum is the distribution of electromagnetic radiation of all possible frequencies and wavelengths.

Electromagnetic spectrum is classified are as follows:

Radio waves:  Frequency of these waves ranges from few Hz to 109 Hz. Radio waves emitted by radio stations. Radio waves are also emitted by stars and gases in space.

Microwaves: Frequency of these waves ranges from109 Hz to 3.0 *1011Hz.The wavelength of microwaves is greater than 1mm and less than 30cm.It is used byastronomers to learn about the structure of nearby galaxies.

Infrared: Frequency of these waves ranges from 3.0 *1011Hz to 109 Hz. The wavelength of infrared is 1nm to 700nm. In space; infrared light helps us map thedust between stars.

Visible: Frequency of these waves ranges from 4.3 *1014 Hz to7.5 * 1014 Hz.The wavelength of visible light is 400nm to 700nm.Our eyes detect visible light. Fireflies, light bulbs, and stars all emit visible light.

Ultraviolet: Frequency of these waves ranges from 7.5 * 1014 Hz to 5.0 *1015 Hz .The wavelength of ultraviolet rays is 400nm to 60nm Ultraviolet radiation is emitted by the Sun and are the reason skin tans and burns. "Hot" objects in space emit UV radiation as well.

X-ray: Frequency of these waves ranges from 5.0 *1015Hz to3.0* 1018 Hz.The wavelength of X-ray is 60nm to 10-8nm. Hot gases in the Universe also emit X-rays.

Gamma ray: Frequency of these waves rangesfrom 3.0*1018 Hz to3.0 * 1022 Hz. The wavelength of Gamma rays is 0.1nm to 10-5nm. Doctors use gamma-ray imaging to see inside body. The biggest gamma-ray generator of all is the Universe.

Wavelets

Wavelets are the disturbance of the point source but the point source is taken in the primary wave front. Wavelets formed by the locus of the virtual source.

Wave lets are of two types:

a. Primary wavelets and

b. Secondary wavelets.

Wave front

During the propagation of the wave, all the particles of the medium which are located at the same distance from the source receive the disturbance simultaneously and vibrate in the same phase. Thus, a wave front of light at any instance is the locus of all particles of the medium vibrating in the same phase at that time. The shape of wave front depends on the nature of source and the disturbance of the wave front from the source. That is wave front. Wave front is the disturbance of the point source. Wave front formed by the locus of the real source. Wave fronts are of three types:

a. Spherical wave front

b. Cylindrical wave front                                   

c. Plane wave front.

Huygens principle

Huygens’s principle states that:

a. Each point on the primary wave front acts as a source of secondary wave lets, sending out disturbance in all direction in a similar manner as the original source of the light does.

b. The new position of the wave front at any instant is given by the forward envelope of the secondary wavelets at that instant.

Consider a point source of light. Let XY be the section of the spherical wave front at any time t. supposed we are interested in finding the new position of the wave front at time t+∆t. to do so, a number of points a,b,c,d are the point taken on the primary wave front. These point acts as the source of secondary wavelets. In time ∆t light will travel a distance c∆t. taking the point a,b,c,d,…as the centre of sphere each of radius c∆t are drawn. The forward enveloped X’Y’ of these spheres give the position of wave front at ∆t +t and called secondary wave front.

Laws of reflection on the basis of wave theory

The advantages of Michelson’s method are:

 The distance between the two stations is very large.

 Images obtained are very bright so that position can be determined accurately.

 There is no measurement of the displacement of image.

 The disadvantages are:

 It is very difficult to maintain the high speed rotation of mirror.

 High speed of the rotation of the mirror can break the mirror.

MECHANICAL WAVE (FULL EXPLANATIONS)

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.....WAVE MOTION.(FULL EXPLANATIONS)

              WAVE MOTION

A wave is the disturbance produce in the medium from an equilibrium condition which travels with the finite velocity in the region of space.Wave motion transfers energy from one point to another, which may or may not displace particles of the medium.

Characteristics of wave motion

a. Particles vibrate about their mean position when disturbance is produced in medium

b. There is transference of energy to the nearest particle as disturbance occurs, which depends    on the nature of the medium.

c. Total displacement of the particle resultant over the one period is zero.

d. Consecutive particles have certain phase difference as vibration occurs.

e. Vibrating particle   posses both kinetic and potential energy.

f. Wave velocity and particle velocity of the medium are different.

The wave motion is divided in to two categories.

They are: Transverse wave motion

               Longitudinal wave motion

Transverse wave motion

If the particles of the medium vibrate perpendicular to the direction of the propagation of the wave, then the wave motion is called transverse wave motion. These waves can propagate through solids and liquids but not through gases, because gases do not possess elastic properties. Examples of these waves are: vibrations in strings, ripples on water surface and electromagnetic waves.

Properties of transverse wave

1. The particles of medium vibrate perpendicularly to the direction of the propagation of wave.

2. The velocity of each particle is maximum at mean position and zero at extreme position.

3 .All the particles in the medium has same amplitude, frequency and time period.

4. Different particles in the medium have different displacement at any instant of time.

Longitudinal wave motion

If the particles of the medium vibrate to the direction of the propagation of the wave, then the wave motion is called longitudinal wave motion. Examples: sound wave Longitudinal waves travel through the medium with the compression and rarefaction. The compression is the region where volume decreases and consequent increase in density and pressure of the medium and in rarefaction there is increase in volume with consequent decrease in density and pressure. Due to the variation in pressure at different region in the medium longitudinal waves are called pressure waves.

Properties of Longitudinal wave

1. The particles of the medium vibrate to the direction of the propagation of the wave.

2. The velocity of each particle is maximum at mean position and zero at extreme position.

3 All the particles in the medium have same amplitude, frequency and time period.

4. All the particles in phase are at distance equal to nλ where n=1, 2, 3 and λ is the wavelength

Superposition of waves

It states that “when two or more than two progressive waves travel in a medium through any point at the same time the net displacement at that point is equal to the vector sum of the individual displacements of the waves at that point”.

The principle of superposition of waves can be explained as:

a. When two waves having same frequency travelling in the same direction meet each other, constructive interference is formed.

b. If there are number of waves, they travel independently and characteristics of the wave remain unchanged.

c. The  resultant intensity at any point in the medium is not equal to sum of intensity of the  two waves .In constructive interference , the total intensity is greater than sum of intensities of individual waves whereas  in destructive  interference the total intensities is less than the sum of individual intensities.

d. Beats are formed when two waves differing in frequency are superimposed.

Interference of waves

Interference is the superposition of  two waves of the same frequency  travelling in the same direction.

Progressive and stationery waves

Progressive wave or travelling wave

A wave  in which crests and trough (in transverse wave)  or  compression  and rarefaction(in longitudinal waves ) travel forward direction  is called progressive wave.

Consider a particle O at origin in the medium. The displacement at any instant of time is given    byy=Asinwt…………..1

Where A is the amplitude, ω is the angular frequency of the wave. Consider a particle P at a distance x from the particle O on its right. Let the wave travel with a velocity v from left to right. Since it takes some time for the disturbance to reach P, its displacement can be written as

y=A sin (ωt - ɸ)……….2

Where ɸ is the phase difference between the particles O and P

 Hence a path difference of x corresponds to a phase difference of 2πx/λ=ɸ

Substituting the value of the ɸ in equation 2

We get,

y=A sin (ωt -2πx/λ)…………….3

Since we have ω=2π/T=2πf

y=Asin{2πtT−2πxλ}$\mathrm{y}=\mathrm{A}\mathrm{s}\mathrm{i}\mathrm{n}\left\{\frac{2\pi \mathrm{t}}{\mathrm{T}}-\frac{2\pi \mathrm{x}}{\lambda }\right\}$

y=Asin2πλ{vt−x}$\mathrm{y}=\mathrm{A}\mathrm{s}\mathrm{i}\mathrm{n}\frac{2\pi }{\lambda }\left\{\mathrm{v}\mathrm{t}-\mathrm{x}\right\}$ ………4

Similarly, for a particle at a distance x to the left of O, the equation for the displacement is   given byy=Asin2πλ{vt−x}$\mathrm{y}=\mathrm{A}\mathrm{s}\mathrm{i}\mathrm{n}\frac{2\pi }{\lambda }\left\{\mathrm{v}\mathrm{t}-\mathrm{x}\right\}$

If the wave travels from right to left in negative x-axis then the equation for the displacement is     given by

y=Asin2πλ{vt+x}$\mathrm{y}=\mathrm{A}\mathrm{s}\mathrm{i}\mathrm{n}\frac{2\pi }{\lambda }\left\{\mathrm{v}\mathrm{t}+\mathrm{x}\right\}$ ……5

This is the expression of the progressive wave equation.

Stationery waves or standing wave

When two progressive waves of the same wavelength and same amplitude travelling with a same speed in opposite direction to each other in a medium are superposed they give rise to wave called stationary wave or standing wave. These waves are called stationery because they seem to be remained stationery and there is no net transfer of the energy.

The superposition of two waves results in the points such that there is no displacement a (i.e amplitude of vibration) a point called nodes and maximum displacement occurs at the point called antinodes.

Property of stationery waves are:

a. Waves do not transmit energy.

b. In these waves, amplitude of vibration is maximum at antinodes and minimum at nodes.

c. Variation in pressure and density is maximum at nodes and minimum at antinodes.

d. Waves remain stationery between the boundaries.

e. All points between two successive notes vibrate simultaneously.

f. The distant between two adjacent nodes or antinodes is λ/2 and the distance between adjacent nodes and antinodes is λ/4

g.The wave profile doesn’t move in the direction of propagation.

Consider the progressive wave of wavelength   amplitude a and velocity v travelling along the positive x-axis

Displacement at any point is given by

y1${\mathrm{y}}_1$=asin2πλ(vt−x)$\sin \frac{2\pi }{\lambda }\left(\mathrm{v}\mathrm{t}-\mathrm{x}\right)$

Where y1${\mathrm{y}}_1$is displacement at time t

  x is distance of the particle from the origin.

Again consider the another wave travelling   in opposite direction with the same velocity v  and amplitude a  in negative x -axis .

y2${\mathrm{y}}_2$=a sin2πλ(vt+x)$\sin \frac{2\pi }{\lambda }\left(\mathrm{v}\mathrm{t}+\mathrm{x}\right)$

Resultant displacement of such wave is given by

Y=y1$\mathrm{Y}={\mathrm{y}}_1$+y2${\mathrm{y}}_2$

             
= asin2πλ(vt−x)$\mathrm{s}\mathrm{i}\mathrm{n}\frac{2\pi }{\lambda }\left(\mathrm{v}\mathrm{t}-\mathrm{x}\right)$ + a sin2πλ(vt+x)$\sin \frac{2\pi }{\lambda }\left(\mathrm{v}\mathrm{t}+\mathrm{x}\right)$                [  since,  sinA$\sin \mathrm{A}$ +sinB$\sin \mathrm{B}$= 2sinA+B2$2\sin \frac{\mathrm{A}+\mathrm{B}}{2}$cosA−B2$\cos \frac{\mathrm{A}-\mathrm{B}}{2}$  ]

=2asin2πvtλcos2πxλ$\mathrm{s}\mathrm{i}\mathrm{n}\frac{2\pi \mathrm{v}\mathrm{t}}{\lambda }\cos \frac{2\pi \mathrm{x}}{\lambda }$

=2a sinwtcoskx$\sin \mathrm{w}\mathrm{t}\cos \mathrm{k}\mathrm{x}$[since,2πvλ=2πf=w]$\left[\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{e},\frac{2\pi \mathrm{v}}{\lambda }=2\pi \mathrm{f}=\mathrm{w}\right]$&2πλ$\frac{2\pi }{\lambda }$=k where k is propagation constant.
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