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question_answer1) Find the (a) maximum frequency, and (b) minimum wavelength of X-rays produced by 30 kV electrons.
question_answer2) The work function of caesium metal is 2.14 eV. When light of frequency 6 x 1014 Hz is incident on the metal surface, photoemission of electrons occurs. What is the (a) maximum kinetic energy of the emitted electrons, (b) stopping potential, and (c) maximum speed of the emitted photoelectrons ?
question_answer3) The photoelectric cut-off voltage in a certain experiment is 1'5 V. What is the maximum kinetic energy of photoelectrons emitted ?
question_answer4) Monochromatic light of wavelength 632-8 nm is produced by a helium-neon laser. The power emitted is 9-42 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 uniform cross-section which is less than the target area), and (c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?
question_answer5) The energy flux of sunlight reaching the surface of the earth is How many photons (nearly) per square metre are incident on the Earth per second ? Assume that the photons in the sunlight have an average wavelength of 550 nm
question_answer6) in an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be V s. Calculate the value of Planck's constant
question_answer7) A 100 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 nm. (a) What is the energy per photon associated with the sodium light ? (b) At what rate are the photons delivered to the sphere ?
question_answer8) The threshold frequency for a certain metal is Hz. If light of frequency 8.2 x 1014 Hz is incident on the metal, predict the cut-off voltage for the photoelectric emission.
question_answer9) The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm ?
question_answer10) Light of frequency Hz is incident on a metal surface. Electrons with a maximum speed of m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?
question_answer11) Light of wavelength 488 nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the cathode, the stopping (cut-off) potential of photoelectrons is 0.38 V. Find the work function of the material from which the cathode is made.
question_answer12) Calculate the (a) momentum, and (b) de Broglie wavelength of the electrons accelerated through a potential difference of 56 V.
question_answer13) What is the (a) momentum, (b) speed, and (c) de Broglie wavelength of an electron with kinetic energy of 120 eV ?
question_answer14) The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which (a) an electron, and (b) a neutron, would have the same de Brogue wavelength.
question_answer15) What is the de Broglie wavelength of (a) a bullet of mass 0.040 kg travelling at the speed of 1.0 km/s, (b) a ball of mass 0.060 kg moving at a speed of 1.0 m/s, and (c) a dust particle of mass drifting with a speed of 2.2 m/s ?
question_answer16) An electron and a photon each have a wavelength of 100 nm. Find (a) their momenta, (b) the energy of the photon, and (c) the kinetic energy of electron.
question_answer17) (a For what kinetic energy of a neutron will the associated de Broglie wavelength be ? (b) Also find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of at 300 K.
question_answer18) Show that the wavelength of electromagnetic radiaion is equal to the de Broglie wavelength of its quantum (photon).
question_answer19) What is the de Broglie wavelength of a nitrogen molecule in air at 300 K ? Assume that the molecule is moving with the root mean square speed of molecules at this temperature. (Atomic mass of nitrogen = 14-0076 u)
question_answer20) (a) Estimate the speed with which electrons emitted from a heated cathode of an evacuated tube impinge on the anode maintained at a potential difference of 500 V with respect to the cathode. Ignore the small initial speeds of the electrons. The 'specific charge? of the electron i.e., its el m is given to be (b) Use the same formula you employ in (a) to obtain electron speed for an anode potential of 10 MV. Do you see what is wrong ? In what way is the formula to be modified ?
question_answer21) (a) A monoenergetic electron beam with electron speed of is subject to a magnetic field of normal to the beam velocity. What is the radius of the circle traced by the beam, given elm for electron equals . (b) Is the formula you employ in (a) valid for calculating radius of the path of a 20 MeV electron beam ? If not, in what way is it modified ?
question_answer22) An electron gun with its anode at a potential of 100 V Ores out electrons in a spherical bulb containing hydrogen gas at low pressure ( of Hg). A magnetic field of 2-83 x 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 elm from the data.
question_answer23) (a) 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 radiation ? (b) From your answer to (a), guess what order of accelerating voltage (for electrons) is required in such a tube.
question_answer24) 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 y-rays of equal energy. What is the wavelength associated with each ? (1 BeV = 109 eV)
question_answer25) 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 kW power, emitting radio waves of wavelength 500 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 Take the area of the pupil to be about 0.4 cm2, and the average frequency of white light to be about 6 x 1014 Hz.
question_answer26) 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 red light of wavelength 6328 Å produced by a He-Ne laser ?
question_answer27) Monochromatic radiation of wavelength 640.2 nm () from a neon lamp irradiates photosensitive material made of caesium or 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 voltage.
question_answer28) 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 : The stopping voltages, respectively, were measured to be: (a) Determine the value of Planck's constant h. (b) Estimate the threshold frequency and work function for the material.
question_answer29) 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 ?
question_answer30) Light of intensity 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 2eV. What is the implication of your answer?
question_answer31) 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) .
question_answer32) (a) Obtain the de Broglie wavelength of a neutron of kinetic energy 150 e. As you have seen in Exercise 44, an electron beam of this energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable ? Explain, . (b) Obtain the de Broglie 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.
question_answer33) An electron microscope uses electrons accelerated by a voltage of 50 kV. Determine the de Broglie 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 ?
question_answer34) The wavelength of a probe is roughly a measure of the size of a structure that it can probe in some detail. The quark structure of protons and neutrons appears at the minute length -scale of or less. This structure was first probed in early 1970's using high energy electron beams produced by a linear accelerator at Stanford, USA. Guess what might have been the order of energy of these electron beams. (Rest mass energy of electron = 0-511 Me V).
question_answer35) Find the typical de Broglie wavelength associated with a He atom in helium gas at room temperature (27°C) and 1 atm pressure ; and compare it with the mean separation between two atoms under these conditions.
question_answer36) Compute the typical de Broglie wavelength of an electron in a metal at 27°C and compare it with the mean separation between two electrons in a metal which is given to be about m.
question_answer37) Answer the following questions : (a) Quarks inside protons and neutrons are thought to carry fractional charges [ e;(-1/3)e]. Why do they not show up in *Millikan's oil-drop experiment ? (b) What is so special about the combination el m ? Why do we not simply talk of e and m separately ? (c) Why should gases be insulators at ordinary pressures and start conducting at very low pressures ? (d) Every metal has a definite work function. Why do all photoelectrons not come out with the same energy if incident radiation is monochromatic ? Why is there an energy distribution of photoelectrons ? (e) The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations : But while the value of is physically significant, the value of v (and therefore, the value of the phase speed ) has no physical significance. Why?
question_answer38) A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to (a)H (b) H1/2 (c)H0 (d) H-1/2
question_answer39) The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 energy is nearly (o) 1.2nm (b) 1.2 x 10-3 nm (c) 1.2 x 10-6 nm (d) 1.2 x 101 nm
question_answer40) Consider a beam of electrons (each electron with energy E0) incident on a metal surface kept in an evacuated chamber. Then (a) no electrons will be emitted as only photons can emit electrons (b) electrons can be emitted but all with an energy, E0 (c) electrons can be emitted with any energy, with a maximum of E0 - ( is the work function) (d) electrons can be emitted with any energy, with a maximum of E0
question_answer41) Consider Fig. 7.14 in the Fundamental Physics for Class. Suppose the voltage applied to A is increased. The diffracted beam will have the maximum at a value of that ( a) will be larger than that earlier value (b) will be the same as the earlier value (c) will be less than the earlier value (d) will depend on the target
question_answer42) A proton, a neutron, an electron and an - particle have same energy. Then their de Broglie wavelengths compare as (a) (b) (c) (d)
question_answer43) An electron is moving with an initial velocity and is in a magnetic field . Then it's de Broglie wavelength (a) remains constant (b) increases with time (c) decreases with time (d) increases and decreases periodically
question_answer44) An electron (mass m) with an initial velocity is in electric field . It?s de Broglie wavelength at time t is given by (a) (b) (c) (d)
question_answer45) An electron (mass m) with an initial velocity is in an electric field If it?s de Brogue wavelength at time is given by (a) (b) (c) (d)
question_answer46) Relativistic corrections become necessary when the expression for the kinetic energy , becomes comparable with mc2, where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron? (a) (b) (c) (d)
question_answer47) Two particles A1 and A2 of masses m1, m2 (m1 > m2) have the same de Broglie wave- length, Then (a) their momenta are the same (b )their energies are the same (c) energy of A1 is less than the energy of A2 (d) energy of A1 is more than the energy of A2
question_answer48) The de Broglie wavelength of a photon is twice the de Broglie wavelength of an electron. The speed of the electron is .Then (a) (b) (c) (d)
question_answer49) Photons absorbed in matter are converted to heat. A source emitting n photon/sec of frequency v is used to convert 1 kg of ice at 0?C to water at 0?C. Then, the time T taken for the conversion (a) decreases with increasing n, with v fixed (b) decreases with n fixed, v increasing (c) remains constant with n and v changing such that = constant (d) increases when the product increases
question_answer50) A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de Broglie wavelength of the particle varies cyclically between two values and.Which of the following statement are true? (a) The particle could be moving in a circular orbit with origin as centre (b) The particle could be moving in an elliptic orbit with origin as its focus (c) When the de Broglie wavelength is, the particle is nearer the origin than when its value is (d) When the de Broglie wavelength is the particle is nearer the origin than when its value is
question_answer51) A proton and an -particle are accelerated, using the same potential difference. How are the de Broglie wavelengths Ay and Ag related to each other?
question_answer52) (i) In the explanation of photo electric effect, we assume one photon of frequency v collides with an electron and transfers its energy. This leads to the equation for the maximum energy of the emitted electron as where g is the work function of the metal. If an electron absorbs 2 photons (each of frequency v ) what will be the maximum energy for the emitted electron? (ii) Why is this fact (two photon absorption not taken into consideration in our discussion of the stopping potential?
question_answer53) There are materials which absorb photons of shorter wavelength and emit photons of longer wavelength. Can there be stable substances which absorb photons of larger wavelength and emit light of shorter wavelength.
question_answer54) Do all the electrons that absorb a photon come out as photoelectrons?
question_answer55) There are two sources of light, each emitting with a power of 100 W. One emits X-rays of wavelength 1 nm and the other visible light at 500 nm. Find the ratio of number of photons of X-rays to the photons of visible light of the given wavelength?
question_answer56) Consider Fig. 7(EP).2 for photoemission. How would you reconcile with momentum-conservation? Note light (photons) have momentum in a different direction than the emitted electrons.
question_answer57) Consider a metal exposed to light of wavelength 600 nm. The maximum energy of the electron doubles when light of wavelength 400 nm is used. Find the work function in eV.
question_answer58) Assuming an electron is confined to a 1 nm wide region, find the uncertainty in momentum using Heisenberg Uncertainty principle (). You can assume the uncertainty in position as 1 nm. Assuming , find the energy of the electron in electron volts.
question_answer59) Two monochromatic beams A and B of equal intensity, hit a screen. The number of photons hitting the screen by beam A is twice that by beam B. Then what inference can you make about their frequencies? i.e., Frequency of beam B is twice of beam A.
question_answer60) Two particles A and B of de Broglie wavelengths and combine to form a particle C. The process conserves momentum. Find the de Broglie wavelength of the particle C. (The motion is one Dimensional).
question_answer61) A neutron beam of energy E scatters from atoms on a surface with a spacing d = 0.1 nm. The first maximum of intensity in the reflected beam occurs at = . What is the kinetic energy E of the beam in ?
question_answer62) Consider a thin target (10-2 m square, 10-3 m thickness) of sodium, which produces a photocurrent of 100 when a light of intensity falls on it. Find the probability that a photoelectron is produced when a photon strikes a sodium atom. [Take density of Na = 0.97 kg/m3, Avogadro's number = 6 x 1026 kg atom],
question_answer63) Consider an electron in front of metallic surface at a distance d (treated as an infinite plane surface). Assume the force of attraction by the plate is given as Calculate work in taking the charge to an infinite distance from the plate. Taking d = 0.1 nm, find the work done in electron volts. [Such a force law is not valid for .
question_answer64) A student performs an experiment on photoelectric effect, using two materials A and B. A plot of is given in Fig. 7(EP).4 (i) Which material A or 5 has a higher work function? (ii) Given the electric charge of an electron = 1.6 x 10-19 C, find the value of h obtained from the experiment for both A and B. Comment on whether it is consistent with Einstein's theory.
question_answer65) A particle A with a mass is moving with a velocity and hits a particle B (mass ) at rest (one dimensional motion). Find the change in the de Broglie wavelength of the particle A. Treat the collision as elastic.
question_answer66) Consider a 20 W bulb emitting light of wavelength 5000 and shinning on a metal surface kept at a distance 2 m. Assume that the metal surface has work function of 2 and that each atom on the metal surface can be treated as a circular disk of radius 1.5. (i) Estimate no. of photons emitted by the bulb per second. [Assume no other losses] (ii) Will there be photoelectric emission? (ii'i) How much time would be required by the atomic disk to receive energy equal to work function ()? (iv)How many photons would atomic disk receive within time duration calculated in (iii) above? (v) Can you explain how photoelectric effect was observed instantaneously? [Hint: Time calculated in part (iii) is from classical consideration and you may further take the target of surface area say 1 cm2 and estimate what would happen ?]
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