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# NCERT Solutions class 12 physics Dual Nature of Radiation and Matter Part 2

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## NCERT Class 12 Physics Chapter-wise Solutions

• 1 – Electric Charges and Fields
• 2 – Electrostatic Potential and Capacitance
• 3 – Current Electricity
• 4 – Moving Charges and Magnetism
• 5 – Magnetism and Matter
• 6 – Electromagnetic Induction
• 7 – Alternating Current
• 8 – Electromagnetic Waves
• 9 – Ray Optics and Optical Instruments
• 10 – Wave Optics
• 11 – Dual Nature of Radiation and Matter
• 12 – Atoms
• 13 – Nuclei
• 14 – Semiconductor Electronic: Material, Devices and Simple Circuits
• 15 – Communication Systems

## CHAPTER 11 DUAL NATURE OF RADIATION AND MATTER

• 11.1 Introduction
• 11.2 Electron Emission
• 11.3 Photoelectric Effect
• 11.4 Experimental Study of Photoelectric Effect
• 11.5 Photoelectric Effect and Wave Theory of Light
• 11.6 Einstein’s Photoelectric Equation: Energy Quantum of Radiation
• 11.7 Particle Nature of Light: The Photon
• 11.8 Wave Nature of Matter
• 11.9 Davisson and Germer Experiment

## NCERT Solutions class 12 physics Dual Nature of Radiation and Matter Part 2

19: 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)

20: (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 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 C.

(b) Use the same formula you employ in (a) 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 modified?

21: (a) A mono-energetic electron beam with electron speed of is subject to a magnetic field of T normal to the beam velocity. What is the radius of the circle traced by the beam, given e/m 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?

[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 emphasize 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.]

22:  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 of Hg). A magnetic field of 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.

23: (a) An X-ray tube produces a continuous spectrum of radiation with its short wavelength end at 0.45 .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?

24:  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? ()

25: 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 radiowaves 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 , and the average frequency of white light to be about .

26: Ultraviolet light of wavelength 2271  ¦ 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 ¦ produced by a He-Ne laser?

27: Monochromatic radiation of wavelength 640.2 nm 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.

28: 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:

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 ). 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.]

29: 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 ¦ 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?

30:  Light of intensity falls on a sodium photo-cell of surface area . 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?

31:  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 ¦, which is of the order of inter-atomic spacing in the lattice) .

32: (a) Obtain the de Broglie wavelength of a neutron of kinetic energy 150 eV. As you have 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.

(b) Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27 ºC). Hence explain why a fast neutron beam needs to be the rmalised with the environment before it can be used for neutron diffraction experiments.

33: 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?

34:  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 10-15m 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.)

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

36:  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.

[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 in distinguish ability has many fundamental implications which you will explore in more advanced Physics courses.]

(a) Quarks inside protons and neutrons are thought to carry fractional charges [(+2/3)e ; ( – 1/3)e]. Why do they not show up in Millikan’s oil-drop experiment?

(b) What is so special about the combination e/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:

, p =

But while the value of  is physically significant, the value of  (and therefore, the value of the phase speed ) has no physical significance. Why?

## NCERT Solutions for Class 12 Physics

NCERT Solutions Class 12 Physics PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 physics includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Physics have total 20 chapters. 12 Physics NCERT Solutions in PDF for free Download on our website. Ncert physics class 12 solutions PDF and physics ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide

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