PHYSICS Pocket diary


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Radioactivity questions with solutions -

What is diffraction


  • It is a common observation with the waves of all kinds that they bend round the edge of an obstacle.

  • Light like other waves also bends round the corner but in comparison to sound waves small bending of light is due to very short wavelength of light which is of the order of 10-5 cm.

  • This effect of bending of light beams round the corner was first discovered by Grimaldi (1618-1663).

  • We now define diffraction of light as phenomenon of bending of light waves around the corners and their spreading into geometrical shadow.

  • Fresnel first explained that the diffraction phenomenon was the result of mutual interference between the secondary wavelets from the same wavefront.

  • Thus we can explain diffraction phenomenon using Huygen's principle.

  • The diffraction phenomenon is usually divided into two classes
    1. Fresnel class of diffraction phenomenon where the source of light and scteen are in general at finite distance from the diffracting aperture
    2. Fraunhofer class of diffraction phenomenon where source and the screen are at the infinite distance from the aperture , this is easily achieved by placing the source of light on the focal plane of a convex lens and placing screen on focal plane of another convex lens. This class of diffraction is simple to treat and easy to observe in practice.

  • Solve out mechanics problems (IITJEE tips and tricks for mechanics)

    Hi all here in this article i am giving some tips and tricks to solve problems in mechanics. To master problem solving skill you need to practice more and more problems as said practice makes a man perfect. Look at examples in your text books identify the steps and then try solving out problems on your own.
     
    Motion in a Two dimensional Plane

    1. Select a coordinate system and resolve the initial velocity vector into x and y components.
    2. Find out acceleration in each direction and solve in each direction according to one rectilinear motion equation.
    3. If the acceleration is in vertical direction only.Follow the techniques for solving constant-velocity problems to analyze the horizontal motion. Follow the techniques for solving constant-acceleration problems to analyze the vertical motion. The x and y motions share the same time of flight t.
    4. There might be question about trajortory in the Problem ,find out the motion in x and y direction with respect to time from previous point.And then find the value of t from one equation and then put that value in another equation to find out the equation of trajactory

    Motion in a Three dimensional Plane
    1. Select a coordinate system and resolve the initial velocity vector into x , y and z components
    2. Find out acceleration in each direction and solve in each direction according to one rectilinear motion equation.

    Uniform Circular Motion
    1. Draw a simple, neat diagram of the system.
    2. Firstly consider the origin of the forces acting on the each object.To do this find out the field forces acting on the each object.Wherever contact in available account the contact force carefully
    3. Find out the force acting on the body.The resultant force should provide the required centrepatal required for Circular motion
    4. Centrepatal force=mv2/R will give the velotiy accordingly
    For more visit http://physicscatalyst.com/articles.php

    Coherent Sources of light


  • Coherent sources are those sources of light which emit continous light waves of same wavelength , same frequency and are in same phase or have constant phase difference.

  • For observing interference phenomenon coherence of light waves is a must.

  • For light waves emitted by two sources of light , to remain coherent the initial phase difference between waves should remain constant in time. If the phase difference changes continously or randomly with time then the sources are incoherent.

  • Two independent sources of light are not coherent and hence can not produce interference because light beam is emitted by millions of atoms radiating independently so the phase difference between waves from such sources fluctuates randomly many times per second.

  • The coherent sources can be obtained either by the source and obtaining its virtual image or by obtaining two virtual images of the same source. This is because any change of phase in real source will cause a simultaneous and equal change in its image.

  • Generally coherence in interference is obtained by two methods
    (1) Division of wave front where wavefront is divided into two parts by reflection, refraction or diffraction and those two parts reunite at a small angle to produce interference as done in case of Young's double slit experiment and Fresnel's biprism experiment.
    (2) Division of amplitude where amplitude of a section of wavefront is divided into two parts and reunited later to produce interference such as in case of thin films.

  • Laser light is almost monochromatic light with little spreading and two independent sources of laser light can produce observable interference pattern.

  • Magnetic field

    We will now look at the properties of the magnetic field which are related to the flux and circullation of the vector field to express the basic laws of magnetic field. We already know how to represent electric field graphically and unlike any other vector field magnetic field B can be represented with the help of field lines drawn in such a way that tangent to those lines at any point concides with the direction of the magnetic field B and the density of the lines is proportional to the magnitude of the vector at a given point. we would now consider the basic laws of magnetic field....
    (1) Gauss's Theorem for the field B:-
    It says that "Flux of B through any closed surface is equal to zero". i.e.,



    This says that field lines of vector B neither begning nor end and therefore field lines of vector B emerging from any volume closed by surface S is always equal to the number of lines entering this volume. This law also indicate the absence of magnetic charges on which field lines of vector B begin or terminate i.e., magnetic fields has no sources as charges are for electric field.

    (2) Theorem of circulation of magnetic field:-
    It states that " Circulation of vector B around a arbitrary contour C is equal to the product of magnetic permeability times the algebric sum of currents enveloped by the contour C".



    The current is assumed to be positive if its direction is connected with the direction of the circumvention of the contour C through the right hand screw rule and is negative if it is in opposite direction. This theorem can be proved by means of Biot Savart's Law. This theorem plays same role for magnetic field as Gauss's theorem plays for electric field.

    For full length notes on magnetic effect of current and magnetism visit http://physicscatalyst.com/

    Rutherford's nucleus model

    According to this model most of the mass of atom and all its positive charge are concentrated in tiny nucleus, and electrons in the atom revolve around it. This model of atomic structure emerged from Geiger - Marsden experiment in 1911 in which a collimated beam of 5.5 MeV alpha particles from bismuth was allowed to fall on 2.1 x 10-7 mm thin gold foil. The scattered alpha particles produced scintillations on ZnS screen, which were counted at different angles (θ) from the direction of the beam.. though most of the alphs particles suffer negligible deviation , some (about one in 104) suffered a large change in direction (θ>90) The last observation gave crutial clue to the nuclear model.
                Rutherford's calculation used the inverse square law of repulsive force between alpha particle and the gold nucleus. Multiple scattering was ignored. The scattering angle θ of alpha particle is related to impact parameter b by the relation
    b=[Ze2 cot(θ/2)]/[4πε0(mv2/2)]
    where impact parameter is defined as the perpandicular distance of the initial velocity vector of the alpha particle from the centre of the nucleus.  The observed number of scattered alpha particles at different angles agreed with Rutherford's calculation based on the nuclear model of atom.
                   Classically Rutherford's model of atom is unstable because an orbiting electron accelerates continously and must loose its energy as EM radiation. The orbit should shrink spiraly into the nucleus within 10-8 sec and gives out continous spectrum of radiation. But we now that hydrogen atom is stable and has a characterstic line spectrum . This difficulty of unstable and shrinking orbits was taken care in Bohr's model of hydrogen atom and would be discussed later.

    CSIR-NET and GATE physics: Electric and Magnetic fields

    CSIR-NET and GATE physics: Electric and Magnetic fields: "We will now discuss electric and magnetic field vectors (E and B)at a point in the absence of charge. Now let us place a charge q at poi..."

    X-Rays FACT FILE

    1. X-Rays are emitted from metal when metal surface is hit by high energy electrons. The electrons penetrate close to the nucleus and displace electrons around the nucleus. The enerfy change is equal to hf where f is the frequency and is very high for radiation emitted.
    2. X-Rays are EM waves of very high frequency and short wavelength near about a 100 times shorter then the wavelength of visible light.
    3. Moseley’s law : Moseley measured the frequencies of characteristic X-rays from large number of elements and plotted the square root of th frequency against its position number in the periodic table.
    His observations are mathematically expressed as
    √(v) = a(Z-b)
    v = the frequency of characteristic X-rays from the elements\
    Z = atomic number
    a, b are constants
    Bragg’s law :Atomic structure of crystals can be studied by X Ray analysis and was started in 1914 by Sir William Bragg with notable achievements.
    Bragg's law is :- 2d sin θ = n λ
    d = interplanar spacing of the crystal on which X-rays are incident
    θ = is the incident angle at which X-rays are strongly reflected.
    n = 1,2,3 …
    λ = wave length of X-rays
    Application of Bragg’s law : By using a monochromatic X-ray beam (having a single wave length) and noting the angles of strong reflection, the interplanar spacing d and several information about the structure of the crystals can be obtained.
    4. x-rays do not contain charged particles. hence they are not deflected by electric or magnetic field.

    5. They effect a photographic plate. The effect is stronger than light.
    6. When incident on certain materials barium platinocyanide, X rays cause fluorescence.

    7. When passed through a gas, X rays ionize the molecules of the gas.


    Light : Waves or particles

    When we think of light a question comes to our mind whether it light is a wave or a particle. This discussion is very interesting and has got a long history. Newton the great physicist tried to understand travel of light in straight line assuming that a luminous body emits very minute and weightless particles called corpuscles travelling through empty space in straight line in all directions with the speed of light and carry kinetic energy with them. Thus energy is carried by stream of particles travelling with a finite velocity , this is the basic principle behind what we call the Corpuscular theory proposed by Sir Issac Newton.  This Corpuscular theory of light can fairly explain the phenomenon of reflection , refraction and rectilinear propagation of light but failed to explain phenomenon of interference , diffraction and polarization of light.
               A new theory of propagation of light was suggested by Dutch physicist Christian Huygens in 1678 in which he suggested that light may be a wave phenomenon produced by mechanical vibrations of an all pervading hypothetical homogeneous medium called ether just like those in liquids and solid. This medium was supposed to be mass less with extremely high elasticity and very low density. In this theory there is a transfer of energy by wave motion without actual travelling of matter. At first wave theory of light was not accepted primarily because of Newton's authority and also because light could travel through vacuum and waves require a medium to propagate from one place to another. Wave theory of light first begin to gain acceptance when double slit experiment of Thomas Young in 1801 firmly established that light is indeed a wave phenomenon. After this double slit interference experiment many experiments were carried out by scientists involving interference and diffraction of light which could only be explained by assuming wave model of light.
              Later on in nineteenth century Maxwell put forward his electromagnetic theory and predicted the existence of electromagnetic waves and calculated the speed of EM waves in free space and fount that this value was very close to the measured value of speed of light in vacuum. He then suggested that light must be an EM wave associated with changing electric and magnetic fields which results the propagation of light or EM waves even in the vacuum. So this way mo material medium is required for the propagation of light wave travelling from one place to another. This fact established that light is a wave phenomenon.
               But this is not the end of the story Hertz first observed the phenomenon of photoelectric effect in1800 according to which when light falls on metal surface , electrons are emitted from the metal surface and the kinetic energy of the electrons does not depend on the intensity of light used. This phenomenon was latter explained successfully by another great physicist Albert Einstein in 1905 by assuming light as photons the quanta of light. His theory again gave rise to the old discussion whether light is a wave or particle. Later on well established particles like electrons also shows diffraction phenomenon under suitable conditions and such effects csn be studied under wave particle duality beyond the scope of this article. 

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