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(i) In Young's double slit experiment, derive the condition for (a) constructive interference and (b) destructive interference at a point on the screen. (ii) A beam of light consisting of two wavelengths, 800 nm and 600 nm is used to obtain the interference fringes on a screen placed 1.4 m away in a Young's double slit experiment. If the two slits are separated by 0.28 mm, calculate the least distance from the central bright maximum where the bright fringes of the two wavelengths

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(i) What is the effect on the interference fringes to a Young's double slit experiment when (a) the separation between the two slits is decreased? (b) the width of the source slit is increased? (c) the monochromatic source is replaced by a source of white light? Justify your answer in each case.(ii) The intensity at the central maxima in Young's double slit experimental set up is `I_0`. Show that the intensity at a point where the path difference is `lambda//3` , is

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State the importance of coherent sources in the phenomenon of interference. In Young's double slit experiment to produce interference pattern, obtain the conditions for constructive and destructive interference. Hence, deduce the expression for the fringe width. How does the fringe width get affected, if the entire experimental apparatus of YDSE is immersed in

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(i) What are coherent sources? Why are they necessary for observing a sustained interference pattern? How are the two coherent sources obtained in the Young's double slit experiment? (ii) Show that the superposition of the waves originating from the two coherent sources, `S_1 and S_2` having displacement, `Y_1 = a cosomegat and Y_2 = a cos(omegat+phi)` at a point produce a resultant intensity, `I = 4a^2 cos^2 phi//2` Hence, write the conditions for the appearance of dark and bright

asked Mar 20, 2022 in 12th Physics by varun (6.7k points)

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In a Young's double slit experiment, (i) deduce the conditions for constructive and destructive interference. Hence, write the expression for the distance between two consecutive bright or dark fringe. (ii) what change in the interference pattern do you observe, if the two slits, `S_1 and S_2` are taken as point sources? (iii) plot a graph of the intensity distribution versus path difference in this experiment. Compare this with the intensity distribution of fringes due to diffraction at a single slit. What important difference do you

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(i) Estimate the speed with which electrons emitted from a heated emitter of an evacuated tube impinge on the collector maintained at a potential difference of 500 V with respect to the emitter. Ignore the small initial speeds of the electrons. The specific charge of the electron, i.e., its e/m is given to be 1.76 × 1011 C kg–1 .(ii) Use the same formula you employ in (i) to obtain electron speed for an collector potential of 10 MV. Do you see what is wrong ? In what way is the formula to be

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(i) A monoenergetic electron beam with electron speed of 5.20 × 106 m s–1 is subject to a magnetic field of 1.30 × 10–4 T normal to the beam velocity. What is the radius of the circle traced by the beam, given e/m for electron equals 1.76 × 1011C kg–1 .(ii) Is the formula you employ in (i) valid for calculating radius of the path of a 20 MeV electron beam? If not, in what way is it modified? [Note: Exercises 20(ii) and 21(ii) take you to relativistic mechanics which is beyond the scope of this book. They have been

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An electron gun with its collector at a potential of 100 V fires out electrons in a spherical bulb containing hydrogen gas at low pressure (∼10–2 mm of Hg). A magnetic field of 2.83 × 10–4 T curves the path of the electrons in a circular orbit of radius 12.0 cm. (The path can be viewed because the gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the ‘fine beam tube’ method.) Determine e/m from the

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An X-ray tube produces a continuous spectrum of radiation with its short wavelength end at 0.45 Å. What is the maximum energy of a photon in the

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From your answer to (i), guess what order of accelerating voltage (for electrons) is required in such a tube

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In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as annihilation of an electron-positron pair of total energy 10.2 BeV into two γ-rays of equal energy. What is the wavelength associated with each γ-ray? (1BeV = 109

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Estimating the following two numbers should be interesting. The first number will tell you why radio engineers do not need to worry much about photons! The second number tells you why our eye can never ‘count photons’, even in barely detectable light. The number of photons emitted per second

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Estimating the following two numbers should be interesting. The first number will tell you why radio engineers do not need to worry much about photons! The second number tells you why our eye can never ‘count photons’, even in barely detectable light. The number of photons entering the pupil

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Ultraviolet light of wavelength 2271 Å from a 100 W mercury source irradiates a photo-cell made of molybdenum metal. If the stopping potential is –1.3 V, estimate the work function of the metal. How would the photo-cell respond to a high intensity (∼105 W m–2) red light of wavelength 6328 Å produced by a He-Ne laser

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Monochromatic radiation of wavelength 640.2 nm (1nm = 10–9 m) from a neon lamp irradiates photosensitive material made of caesium on tungsten. The stopping voltage is measured to be 0.54 V. The source is replaced by an iron source and its 427.2 nm line irradiates the same photo-cell. Predict the new stopping

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A mercury lamp is a convenient source for studying frequency dependence of photoelectric emission, since it gives a number of spectral lines ranging from the UV to the red end of the visible spectrum. In our experiment with rubidium photo-cell, the following lines from a mercury source were used: λ1 = 3650 Å, λ2 = 4047 Å, λ3 = 4358 Å, λ4 = 5461 Å, λ5 = 6907 Å, The stopping voltages, respectively, were measured to be: `V_01` = 1.28 V,`V_02` = 0.95 V, `V_03` = 0.74 V, `V_04` = 0.16 V, `V_05` = 0 V Determine the value of

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The work function for the following metals is given: Na: 2.75 eV; K: 2.30 eV; Mo: 4.17 eV; Ni: 5.15 eV. Which of these metals will not give photoelectric emission for a radiation of wavelength 3300 Å from a He-Cd laser placed 1 m away from the photocell? What happens if the laser is brought nearer and placed 50 cm away

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Light of intensity 10–5 W m–2 falls on a sodium photo-cell of surface area 2 cm2 . Assuming that the top 5 layers of sodium absorb the incident energy, estimate time required for photoelectric emission in the wave-picture of radiation. The work function for the metal is given to be about 2 eV. What is the implication of your

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Crystal diffraction experiments can be performed using X-rays, or electrons accelerated through appropriate voltage. Which probe has greater energy? (For quantitative comparison, take the wavelength of the probe equal to 1 Å, which is of the order of inter-atomic spacing in the lattice) (me =9.11 × 10–31

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Obtain the de Broglie wavelength of a neutron of kinetic energy 150 eV. As you have seen in Exercise .31, an electron beam of this energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable? Explain. (mn = 1.675 × 10–27

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