Find the (I) maximum frequency,and (II) minimum wavelength of X-rays produced by 30 kV electrons.

The work function of caesium metal is 2.14 eV. When light of frequency 6 ×10¹⁴ Hz is incident on the metal surface, photoemission of electrons occurs. What is the (I) maximum kinetic energy of the emittedelectrons, (II) Stopping potential,and (III) maximum speed of the emitted photoelectrons?

The photoelectric cut-off voltage in a certain experiment is 1.5 V. What is the maximum kinetic energy of photoelectrons emitted?

Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. The power emitted is 9.42 mW. (I) Find the energy and momentum of each photon in the lightbeam, (II) Howmanyphotonspersecond,ontheaverage,arriveatatargetirradiatedbythis beam? (Assume the beam to have uniform cross-section which is less than the target area),and (III) Howfastdoesahydrogenatomhavetotravelinordertohavethesamemomentum as that of thephoton?

Theenergyfluxofsunlightreachingthesurfaceoftheearthis1.388×10³W/m².How manyphotons(nearly)persquaremetreareincidentontheEarthpersecond?Assume that the photons in the sunlight have an average wavelength of 550nm.

In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be 4.12 × 10^-15 V s. Calculate the value of Planck’s constant.

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?

The threshold frequency for a certain metal is 3.3 × 1014 Hz. If light of frequency 8.2 × 1014 Hz is incident on the metal, predict the cutoff voltage for the photoelectric emission.

The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?

Light of frequency 7.21 × 10¹⁴ Hz is incident on a metal surface. Electrons with a maximum speed of 6.0 × 10⁵ m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?

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 emitter, the stopping (cut-off) potential of photoelectrons is 0.38 V. Find the work function of the material from which the emitter is made.

Calculate the (I) momentum,and (II) deBrogliewavelengthoftheelectronsacceleratedthroughapotentialdifferenceof 56V.

What is the (I) momentum, (II) speed,and (III) de Broglie wavelength of an electron with kinetic energy of 120eV.

The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which (I) an electron,and (II) a neutron, would have the same de Broglie wavelength.

What is the de Broglie wavelength of (I) a bullet of mass 0.040 kg travelling at the speed of 1.0km/s, (II) a ball of mass 0.060 kg moving at a speed of 1.0 m/s,and (III) a dust particle of mass 1.0 × 10^-9 kg drifting with a speed of 2.2m/s?

An electron and a photon each have a wavelength of 1.00 nm. Find (I) theirmomenta, (II) the energy of the photon,and (III) the kinetic energy of electron.

(I) ForwhatkineticenergyofaneutronwilltheassociateddeBrogliewavelengthbe 1.40 × 10^-10m? (II) AlsofindthedeBrogliewavelengthofaneutron,inthermalequilibriumwithmatter, having an average kinetic energy of (3/2) kT at 300K.

Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).

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)

(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 withrespecttotheemitter.Ignorethesmallinitialspeedsoftheelectrons.Thespecific charge of the electron, i.e., its e/m is given to be 1.76 × 10¹¹ Ckg^-1. (II) Usethesameformulayouemployin(a)toobtainelectronspeedforancollector potential of 10 MV. Do you see what is wrong? In what way is the formula to be modified?

(I) Amonoenergeticelectronbeamwithelectronspeedof5.20×10⁶ms^-1issubjectto 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 × 10¹¹ Ckg^-1. (II) Istheformulayouemployin(a)validforcalculatingradiusofthepathofa20MeV electron beam? If not, in what way is itmodified? [Note: Exercises 11.20(b) and 11.21(b) take you to relativistic mechanics which is beyond the scope of this book. They have been inserted here simply to emphasise the point that the formulas you use in part (a) of the exercises are not valid at very high speeds or energies. See answers at the end to know what ‘very high speed or energy’ means.]

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 data.

(I) AnX-raytubeproducesacontinuousspectrumofradiationwithitsshortwavelength end at 0.45 Å. What is the maximum energy of a photon in theradiation? (II) Fromyouranswerto(a),guesswhatorderofacceleratingvoltage(forelectrons)is required in such atube?

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 ?-rays of equal energy. What is the wavelength associated with each ?-ray? (1BeV = 10⁹ eV)

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. (I) ThenumberofphotonsemittedpersecondbyaMediumwavetransmitterof10kW power, emitting radiowaves of wavelength 500m. (II) Thenumberofphotonsenteringthepupilofoureyepersecondcorrespondingto theminimumintensityofwhitelightthatwehumanscanperceive(~10^-10Wm^-2).Take the area of the pupil to be about 0.4 cm², and the average frequency of white light to be about 6 × 10¹⁴ Hz.

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?

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 voltage.

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: ?₁ = 3650 Å, ?₂= 4047 Å, ?₃= 4358 Å, ?₄= 5461 Å, ?₅= 6907 Å, The stopping voltages, respectively, were measured to be: V₀₁ = 1.28 V, V₀₂ = 0.95 V, V₀₃ = 0.74 V, V₀₄ = 0.16 V, V₀₅ = 0 V Determine the value of Planck’s constant h, the threshold frequency and work function for the material. [Note: You will notice that to get h from the data, you will need to know e (which you can take to be 1.6 × 10^-19 C). Experiments of this kind on Na, Li, K, etc. were performed by Millikan, who, using his own value of e (from the oil-drop experiment) confirmed Einstein’s photoelectric equation and at the same time gave an independent estimate of the value of h.]

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?

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 answer?

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) (m_e= 9.11 × 10^-31 kg).

(I) ObtainthedeBrogliewavelengthofaneutronofkineticenergy150eV.Asyouhave seen in Exercise 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. (m_n= 1.675 × 10^-27kg) (II) Obtain the de Broglie wavelength associated with thermal neutrons at room temperature(27ºC).Henceexplainwhyafastneutronbeamneedstobethermalised with the environment before it can be used for neutron diffractionexperiments.

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?

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 10^-15 m 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 MeV.)

Find the typical de Broglie wavelength associated with a He atom in helium gas at room temperature (27 ºC) and 1 atm pressure; and compare it with the mean separation between two atoms under these conditions.

Compute the typical de Broglie wavelength of an electron in a metal at 27 ºC and compare it with the mean separation between two electrons in a metal which is given to be about 2 × 10^-10 m. [Note: Exercises 11.35 and 11.36 reveal that while the wave-packets associated with gaseous molecules under ordinary conditions are non-overlapping, the electron wave- packets in a metal strongly overlap with one another. This suggests that whereas molecules in an ordinary gas can be distinguished apart, electrons in a metal cannot be distinguished apart from one another. This indistinguishibility has many fundamental implications which you will explore in more advanced Physics courses.]