Physics

An electron microscope uses electrons accelerated by a voltage of 50 \mathrm{kV}. Determine the de B roglie wavelength associated with the electrons. If other factors (such as numerical aperture, etc.) are taken to be roughly the same, how does the resolving power of an electron microscope compare with that of an optical microscope which uses yellow light?

Electrons are accelerated by a voltage of $50 \mathrm{kV}$ Charge on an electron, $e=1.6 \times 10^{-19} \mathrm{C}$ Mass of the electron, $m_{e}=9.11 \times 10^{-31} \mathrm{~kg}$ Wavelength of the...

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(a) Obtain the de Broglie wavelength of a neutron of kinetic energy 150 \mathrm{eV}. As you have seen in question 11.31, an electron beam of this energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable? Explain. \left(m_{n}=1.675 \times 10^{-27} \mathrm{~kg}\right).
(b) Obtain the de B roglie wavelength associated with thermal neutrons at room temperature (27 °C). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.

(a) Kinetic energy of the neutron is given as $=150 \mathrm{eV}$ $=150 \times 1.6 \times 10^{-19}$ $=2.4 \times 10^{-17} \mathrm{~J}$ Mass of the neutron, $m_{n}=1.675 \times 10^{-27} \mathrm{~kg}$...

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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 \AA, which is of the order of interatomic spacing in the lattice) \left(m_{e}=9.11 \times 10^{-31} \mathrm{~kg}\right)

For Electrons, we have the relation for kinetic energy as,$\mathrm{K} . \mathrm{E}=(1 / 2) \mathrm{m}_{\mathrm{e}} \mathrm{V}^{2}$ $=\left(\mathrm{m}_{\mathrm{e}} \mathrm{V}\right)^{2} / 2...

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

Intensity of the light is given as $=10^{-5} \mathrm{~W} \mathrm{~m}^{-2}$ Surface area of the sodium photocell is given as $A=2 \mathrm{~cm}^{2}$ Incident power of the light is given by the...

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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 \mathrm{eV} . Which of these metals will not give photoelectric emission for radiation of wavelength 3300 \AA from a He-Cd laser placed 1 m away from the photocell? What happens if the laser is brought nearer and placed 50 \mathrm{~cm} away?

Wavelength is given as $\lambda=3300 \AA$ Speed of light $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ Planck's constant $=6.63 \times 10^{-34} \mathrm{~J} \mathrm{~s}$ Energy of the photon of the...

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A mercury lamp is a convenient source for studying the 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:
\lambda_{1}=3650 \AA \lambda_{2}=4047 \AA \lambda_{3}=4358 \AA \lambda_{4}=5461 \AA, \lambda_{5}=6907 \AA. The stopping voltages, respectively, were measured to be: \mathbf{V}_{01}=1.28 \mathrm{~V}, \mathrm{~V}_{02}=0.95 \mathrm{~V}, \mathrm{~V}_{03}=0.74 \mathrm{~V}, \mathrm{V}_{04}=0.16 \mathrm{~V}, \mathrm{~V}_{05}=0 \mathrm{~V}.Determine the value of Planck’s constant \mathrm{h}, the threshold frequency and work function for the material.

The following relation can be derived from photoelectric effect,$eV_{o}=hv-\phi_{o}$ Work function of the metal, $\Phi_{0}=\mathrm{hv}-\mathrm{eV}_{0}$ $\Phi_{0}=(h c / \lambda)-e V_{0}$...

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

Wavelength of the monochromatic radiation is given as $\lambda=640.2 \mathrm{~nm}=640.2 \times 10^{-9} \mathrm{~m}$ Stopping potential of the neon lamp is also given as $V_{0}=0.54 \mathrm{~V}$...

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Ultraviolet light of wavelength 2271 \AA from a 100 \mathrm{~W} mercury source irradiates a photo-cell made of molybdenum metal. If the stopping potential is -1.3 \mathrm{~V}, estimate the work function of the metal. How would the photo-cell respond to high intensity \left(\sim 10^{5} \mathrm{~W} \mathrm{~m}^{-2}\right) red light of wavelength 6328 \AA produced by a He-Ne laser?

Wavelength of ultraviolet light is given as $\lambda=2271 \AA{A}=2271 \times 10^{-10} \mathrm{~m}$ Stopping potential of the metal is given as $\mathrm{V}_{0}=1.3 \mathrm{~V}$ Planck's constant,...

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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. (a) The number of photons emitted per second by a Medium wave transmitter of 10 \mathrm{~kW} power, emitting radio waves of wavelength \mathbf{5 0 0} \mathbf{~ m}.
(b) The number of photons entering the pupil of our eye per second corresponding to the minimum intensity of white light that we humans can perceive \left(\sim 10^{-10} \mathrm{~W} \mathrm{~m}^{-2}\right) . Take the area of the pupil to be about 0.4 \mathrm{~cm}^{2}, and the average frequency of white light to be about 6 \times 10^{14} \mathrm{~Hz}

(a) Power of the medium wave transmitter is given as $\mathrm{P}=10 \mathrm{~kW}=10^{4} \mathrm{~W}$ Energy emitted by the transmitter per secon is $E=10^{4}$ Wavelength of the radio waves is given...

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In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as the annihilation of an electron-positron pair of total energy 10.2 BeV into two y-rays of equal energy. What is the wavelength associated with each y-ray? \left(1 \mathrm{BeV}=10^{9} \mathrm{eV}\right)

Total energy of the electron-positron pair is given as $\mathrm{E}=10.2 \mathrm{BeV}=10.2 \times 10^{9} \mathrm{eV}=10.2 \times 10^{9} \times 1.6 \times 10^{-19} \mathrm{~J}$ Hence the energy of...

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(a) An X-ray tube produces a continuous spectrum of radiation with its short wavelength end at 0.45 \AA. What is the maximum energy of a photon in the radiation?
(b) From your answer to (a), guess what order of accelerating voltage (for electrons) is required in such a tube?

(a) Wavelength produced by the $X$-ray tube is given to us as $\lambda=0.45 \AA=0.45 \times 10^{-10} \mathrm{~m}$ Speed of light, $c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ Planck's constant,...

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An electron gun with its collector at a potential of 100 \mathrm{~V} fires out electrons in a spherical bulb containing hydrogen gas at low pressure \left(\sim 10^{-2} \mathrm{~mm}\right. of \mathrm{Hg} ). A magnetic field of 2.83 \times 10^{-4} \mathrm{~T} curves the path of the electrons in a circular orbit of radius 12.0 \mathrm{~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 data.

Potential of the collector is given as $V=100 \mathrm{~V}$ Magnetic field experienced by the electron is given as $\mathrm{B}=2.83 \times 10^{-4} \mathrm{~T}$ Radius of the circular orbit is given...

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(a) A monoenergetic electron beam with an electron speed of 5.20 \times 10^{6} \mathrm{~m} \mathrm{~s}^{-1} is subject to a magnetic field of 1.30 \times 10^{-4} \mathrm{~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 \times 10^{11} \mathrm{C} \mathrm{kg}^{-1}.

(b) Is the formula you employ in (a) valid for calculating the radius of the path of a 20 \mathrm{MeV} electron beam? If not, in what way is it modified?

Magnetic field experienced by the electron, $B=1.30 \times 10^{-4} \mathrm{~T}$ Specific charge, e/m is given by $=1.76 \times 10^{11} \mathrm{Ckg}^{-1}$ Here, $e=$ charge on the electron $=1.6...

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(a) 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 \mathrm{~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 \times 10^{11} \mathrm{C} \mathrm{kg}^{-1}.
(b) Use the same formula you employ in (a) to obtain electron speed for a collector potential of 10 \mathrm{MV}. Do you see what is wrong? In what way is the formula to be modified?

(a) Potential difference of the evacuated tube is given as $500 \mathrm{~V}$ Specific charge of the electron is given as $\mathrm{e} / \mathrm{m}=1.76 \times 10^{11} \mathrm{C} \mathrm{kg}^{-1}$...

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(a) For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 x 10-10 m?
(b) Also find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of (3 / 2) \mathrm{kT} at 300 \mathrm{~K}.

(a) de Broglie wavelength of the neutron is given as $\lambda=1.40 \times 10^{-10} \mathrm{~m}$ Mass of a neutron, $m_{n}=1.66 \times 10^{-27} \mathrm{Kg}$ Planck's constant, $h=6.63 \times 10^{-34}...

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The calorific value and ignition temperature of fuel A are 55kJ/g and 80 degree Celsius respectively. These values for fuel B are 80kJ/g and 10 degree Celsius respectively. On burning, the fuel A produces CO2 and H2O while the fuel B produces CO2, CO, and SO2. Give three points of relative advantages and disadvantages of these two fuels.

Answer: Fuel-A i) It has a low calorific value of 55kJ/g, which is a drawback. ii) The ignition temperature is 80°C, which is moderate and advantageous. iii) No hazardous gases are created, which is...

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A 100W sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is 589 nm. (a) What is the energy per photon associated with the sodium light? (b) At what rate are the photons delivered to the sphere?

Power of the sodium lamp is given as $\mathbf{P}=\mathbf{1 0 0 W}$Wavelength of the emitted sodium light is given as $\lambda=589 \mathrm{~nm}$$$=589 \times 10^{-9} \mathrm{~m}$$Planck's constant,...

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A uniform magnetic field of 1.5 \mathrm{~T} exists in a cylindrical region of a radius of 10.0 \mathrm{~cm}, its direction parallel to the axis along east to west. A wire carrying a current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if, the wire in the N-S direction is lowered from the axis by a distance of 6.0 \mathrm{~cm} ?

When the wire is lowered by $6 \mathrm{~cm}$, then Then, $x=\sqrt{(10)^{2}-\left(6^{2}\right)}=\sqrt{64}=8 \mathrm{~cm}$ $2 \mathrm{x}=\mathrm{I}_{2}=16 \mathrm{~cm}$ $F_{2}=BII_{2}$=$1.5 \times 7...

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Answer the following question:
An electron travelling west to east enters a chamber having a uniform electrostatic field in the north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight-line path.

Because of the electric field, the negatively charged electron tends to go towards the north. The electron will not be deflected if an equal magnetic force acts in the other direction. We derive the...

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Light of wavelength 488 \mathrm{~nm} is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is 0.38 \mathrm{~V}. Find the work function of the material from which the emitter is made.

Wavelength of light produced by the argon laser is given as $\lambda=488 \mathrm{~nm}=488 \times 10^{-9} \mathrm{~m}$ Stopping potential of the photoelectrons is given as...

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A 100 \mathrm{~W} sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength
of the sodium light is 589 \mathrm{~nm} . (a) What is the energy per photon associated with the sodium light? (b) At what rate are the photons delivered to the sphere?

Power of the sodium lamp is given as $\mathbf{P}=\mathbf{1 0 0 W}$ Wavelength of the emitted sodium light is given as $\lambda=589 \mathrm{~nm}$ $=589 \times 10^{-9} \mathrm{~m}$ Planck's constant,...

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The image of a candle flame formed by a lens is obtained on a screen placed on the other side of the lens. If the image is three times the size of the flame and the distance between the lens and image is 80 cm, at what distance should the candle be placed from the lens? What is the nature of the image at a distance of 80 cm and the lens?

                 Ray Diagram The image in the screen is real and so, the magnification is, m = –3 v = 80 cm u = ? m = v/u –3 = 80/u u = –80/3 cm As we know, 1/f = 1/v – 1/u =1/80 + 3/80 = 4/80 =...

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Sudha finds out that the sharp image of the window pane of her science laboratory is formed at a distance of 15 cm from the lens. She now tries to focus the building visible to her outside the window instead of the window pane without disturbing the lens. In which direction will she move the screen to obtain a sharp image of the building? What is the approximate focal length of this lens?

To get a clear picture of the structure, Sudha has to move the screen and remove the lens. The length of the area will be about 15 cm. The light rays from a distant object such as a tree or a...

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A pencil, when dipped in water in a glass tumbler, appears to be bent at the interface of air and water. Will the pencil appear to be bent to the same extent, if instead of water we use liquids like, kerosene or turpentine. Support your answer with reason.

The bending of light here is a reversal function. Reversal is based on refractive indices. The opposing indices of paraffin or turpentine will not be the same as water. So the degree of bending will...

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A child is standing in front of a magic mirror. She finds the image of her head bigger, the middle portion of her body of the same size and that of the legs smaller. The following is the order of combinations for the magic mirror from the top.

(a) Plane, convex and concave (b) Convex, concave and plane (c) Concave, plane and convex (d) Convex, plane and concave Answer: (c) Concave, plane and convex Explanation: Concave mirror showed her...

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Monochromatic light of wavelength 632.8 \mathrm{~nm} is produced by a helium-neon laser. The power emitted is 9.42 \mathrm{~mW} (a) Find the energy and momentum of each photon in the light beam
(b) How many photons per second, on the average, arrive at a target irradiated by this beam? (Assume the beam to have a uniform cross-section which is less than the target area)

Wavelength of a monochromatic light is given as $\lambda=632.8 \mathrm{~nm}=632.8 \times 10^{-9} \mathrm{~m}$ Power emitted by the laser is, $P=9.42 \mathrm{~mW}=9.42 \times 10^{-3} \mathrm{~W}$...

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