Bihar Board - Class 12 Physics - Chapter 11: Dual Nature Of Radiation And Matter Long Answer Question
Long Answer Type Questions
1. What is electron emission ? Define process of electron emission.
Electron Emission:In metal, electrons are quite free to move easily within the metal. These electrons are responsible for the conductivity of metals. These electrons in the outer shell of the atoms are loosely bound. These loosely bound electrons are called free electrons.
If it has got sufficient energy to overcome the attractive pull then only the electron can come out of the metal surface. This phenomenon of emission of electrons from the metal surface is called electron emission.
Process of Electron Emission:
(i). Thermionic emission:
The process of emission of electrons when a metal is heated is known as thermionic emission. The emitted electrons are called thermions. Emitted number of thermions depends on the temperature of the metal surface.
(ii). Field emission:
The process of emission of free electrons when a strong electric field (108 V/m) is applied across the metal surface is known as field emission. Field emission is also known as cold emission or cold cathode emission. One of the examples of cold emission is the spark plug.
(iii). Photoelectric emission:
The process of emission of electrons when the light of suitable frequency is incident on a metal surface is known as photoelectric emission. These photo-generated electrons are called photoelectrons. The number of photoelectrons emitted depends on the intensity of the incident light.
2. What is the photoelectric effect? Give laws of photoelectric emission.
Photoelectric Effect:
The phenomenon of emission of electrons from (preferably) metal surfaces exposed to light energy of suitable frequency is known as the photoelectric effect. The emitted electrons are called photoelectrons and the current produced is called photoelectric current. Alkali metals (lithium, sodium, potassium, cesium, etc.) show a photoelectric effect with visible light.
Laws of photoelectric emission:
The photoelectric current is directly proportional to the intensity of incident radiation.
Saturation current is found to be proportional to the intensity of incident radiation whereas the stopping potential is independent of its intensity.
The maximum kinetic energy or equivalently stopping potential above the threshold frequency of the emitted photoelectrons increases linearly with the frequency of the incident radiation but is not a function of intensity.
Photoelectric emission is an instantaneous process. The time lag is very small between the incidence of radiation and emission of photoelectrons (~10–9 s or less), even when the incident radiation is extremely dim.
3. Discuss Einstein’s Photoelectric Equation.
Einstein’s Photoelectric Equation:
To explain the photoelectric effect in 1905, Albert Einstein proposed a completely different picture of electromagnetic radiation. In this picture radiation energy is built up of discrete units and photoelectric emission does not take place by continuous absorption of energy from radiation. These discrete units are called quanta of energy of radiation. Each quantum of energy is hν, where v is the frequency of light and h is Planck’s constant.
In the photoelectric effect, an electron absorbs a quantum of energy (hv) of radiation. If this absorbed energy exceeds the minimum energy (work function 'w' of the metal), the most loosely bound electron will emerge with maximum kinetic energy, more tightly bound electron will emerge with kinetic energies less than the maximum value.
Einstein’s photoelectric equation
Ek=h-
Ek=h-h0
Ek=h(-0)
4. Define particle Nature of Light.
Particle Nature of Light:
The photoelectric effect thus gave evidence to the strange fact that light in interaction with matter behaved as if it was made of quanta or packets of energy, each of energy hv. A definite value of energy, as well as momentum, is associated with a particle. This particle was later named photon.
We can summarize the photon picture of electromagnetic radiation as follows:
- In the interaction of radiation with matter, radiation behaves as if it is made up of particles called photons.
- Each photon has energy E (=hv) and momentum p (= hv/c), and speed c, the speed of light.
- All photons of light of a particular frequency v, or wavelength λ, have the same energy E (=hv = hc/λ) and momentum p (= hv/c = h/λ). Photons are electrically neutral and are not deflected by electric and magnetic fields.
- In a photon-particle collision (such as a photon-electron collision), the total energy and total momentum are conserved.
5. Explain Davisson and Germer Experiment.
Davisson and Germer Experiment:
The wave nature of electrons was first experimentally verified independently by C. J. Davisson and L. H. Germer in 1927 and by G. P. Thomson in 1928 while observing diffraction effects with beams of electrons scattered by crystals. The experimental arrangement is schematically shown in the figure.
It has an electron gun made up of a tungsten filament F, heated by a low voltage battery and the filament is coated with barium oxide. Emitted electrons from filament are accelerated to a desired velocity by applying the required potential/voltage from a high-voltage power supply. C is a hollow metallic cylinder with a hole along the axis and is kept at a negative potential to get a convergent beam of electrons emitted from the filament. It acts as a cathode. A is a cylinder with a fine hole along its axis acting as an anode.
The cathode and anode form an electron gun by which a fine beam of electrons can be obtained at different velocities by applying different accelerating potentials. N is a nickel crystal cut along a cubical diagonal, and D is an electron detector that can be rotated on a circular scale and is connected to a sensitive galvanometer that records the current.
Working: From the electron gun a fine beam of accelerated electrons is made to fall normally on the surface of the nickel crystal. The atoms of the crystal scatter the incident electrons in different directions. The detector detects the intensity of the electron beam scattered in a particular direction by rotating the electron detector on the circular scale at different positions.
According to de Broglie's hypothesis, the wavelength of the wave associated with the electron is given by
=12.27VA。
6. Show mathematically how Bohr’s postulate of quantization of orbital angular momentum in a hydrogen atom is explained by de Broglie’s hypothesis.
Answer:
According to de Broglie’s hypothesis,
λ = hmv …………………………… (1)
According to de Broglie’s condition of stationary orbits, the stationary orbits are those which contain complete de Broglie wavelengths.
2πr = nλ …………………………………… (2)
Substituting value of λ from (1) in (2), we get
2πr = n hmv
⇒ mvr = n h2 ……………………………………… (3)
This is Bohr’s postulate of quantization of energy levels.
7. (i) Describe briefly three experimentally observed features in the phenomenon of photoelectric effect.
(ii) Discuss briefly how wave theory of light cannot explain these features.
Answer:
(i) Three experimentally observed features in the phenomenon of photoelectric effect are as follows :
- Intensity: When intensity of incident light increases as one photon ejects one electron, the increase in intensity will increase the number of ejected electrons. Frequency has no effect on photoelectrons.
- Frequency: When the frequency of incident photons increases, the kinetic energy of the emitted electrons increases. Intensity has no effect on kinetic energy of photoelectrons.
No Time Lag: When the energy incident photon is greater than the work function, the photoelectron is immediately ejected. Thus, there is no time lag between the incidence of light and emission of photoelectrons.
(ii) These features cannot be explained in the wave theory of light because wave nature of radiation cannot explain the following :
- The instantaneous ejection of the photoelectrons.
- The existence of threshold frequency for a metal surface.
- The fact that kinetic energy of the emitted electrons is independent of the intensity of light and depends upon its frequency.
8. A beam of monochromatic radiation is incident on a photosensitive surface. Answer the following questions :
(i) Do the emitted photoelectrons have the same kinetic energy?
(ii) Does the kinetic energy of the emitted electrons depend on the intensity of incident radiation?
(iii) On what factors does the number of emitted photoelectrons depend?
Answer:
In photoelectric effect, an electron absorbs a quantum of energy hv of radiation, which exceeds the work function, an electron is emitted with maximum kinetic energy.
Ek max = hv – W
(i) No, all electrons are bound with different forces in different layers of the metal. So, more tightly bound electrons will emerge with less kinetic energy. Hence, all electrons do not have the same kinetic energy.
(ii) No, because an electron cannot emit out if quantum energy hv is less than the work function of the metal. The KE depends on the energy of each photon.
(iii) Number of emitted photoelectrons depends on the intensity of the radiations provided the quantum energy hv is greater than the work function of the metal.
9.Explain two ways of emission of electrons from metal surfaces.
Answer: Electrons can be emitted from metal surface by two ways:
Photoelectric emission. If radiation of frequency above a certain minimum frequency called threshold frequency is incident on the surface, electrons are emitted. Such electrons are called photoelectrons and the phenomenon is called photoelectric effect.
Thermoelectric emission is the process of emission of electrons when a metal surface is strongly heated. Such electrons are called thermal electrons.
10. State the dependence of work function on kinetic energy of electrons emitted in a photocell. If the intensity of the incident radiation is doubled, what changes occur in the stopping potential and photoelectric current?
Answer:
For a given frequency v of the incident radiation, the stopping potential V0 is related to the maximum K.E. of the photoelectron which has been just stopped from reaching the collecting plate.
Maximum K.E. of the electron
= 12mvmax 2 ,
where m is the mass of the electron and vmax , the maximum velocity of the emitted electron. If e is the charge on electron then
eV0 = 12mvmax 2
If the intensity of radiation is doubled, the number of photons available will be doubled and hence photoelectric current will be doubled but since vmax remains the same even on doubling the intensity, hence stopping potential will remain constant.
11. Discuss the dual nature of radiations.
Answer: Dual Nature of Radiation:
According to the wave theory, the radiant energy spreads out continuously in the form of waves but according to the quantum theory, the radiant energy spreads out in discrete packets (or quanta) each having the energy hv, where v is the frequency of the radiation and h is the Planck's constant. Its value is 6.624 x 10-34 Js. These two theories are apparently contradictory. Some of the experimental observations can be explained on the basis of one theory and some other observations can be explained by the second theory. Therefore, one theory could not be rejected in favor of the other. With the development of quantum mechanics and experimental observations, the dual nature of radiation has been established. In other words, radiation behaves sometimes as waves and sometimes as particles. Thus, it is said to have dual nature.
12. Define the term threshold frequency and stopping potential in relation to the phenomenon of photoelectric effect. How is the photoelectric current affected on increasing the
(i) frequency
(ii) intensity of incident radiation and why?
Answer:
Threshold frequency: The minimum value of frequency of incident radiation below which photoelectric emission stops altogether is called Threshold frequency.
Stopping potential: The value of retarding potential at which the photoelectric current becomes zero is called stopping potential for the given frequency of incident radiations.
When the frequency of incident radiation is increased (at constant intensity of radiation), the photoelectric current remains constant.
When intensity of incident radiation is increased, there is an increase in the number of photons falling on the surface of photosensitive material and hence photoelectric current increases with intensity of radiation.
13. In Davisson and Germer experiment, states the observation which led to (i) show the wave nature of electrons and (ii) confirm the de-Broglie relation.
Answer: (ii) A fine beam of accelerated electrons is made to fall on nickel crystal and the intensity of electron beam scattered in the given direction is detected for different values of Φ. Graphs are plotted between I and Φ and a bump is observed at accelerating voltage 54 V and Φ = 50°. This bump is due to constructive interference of electrons scattered from different layers of regularly spaced atoms of the crystal. This establishes the wave nature of electrons.
(ii) From Bragg’s law for first order diffraction 2d sin θ = λ
For Ni crystal d = 0.91 Å and θ = 65°
so λ = 2 x 0.91 x sin 65° = 1.65 Å
According to de-Broglie hypothesis, the wavelength of electron in a p.d. 54 V is
λ = 12.2754 Å = 1.66 Å
So there is close agreement with the estimated value of de-Broglie wavelength and the experimental value given by the Davisson-Germer method. This confirms the de-Broglie relation for electrons in motion.
14. Plot a graph showing the variation of stopping potential with the frequency of incident radiation for two different photosensitive materials having work functions and W2(W1 > W2). On what factors does the (i) slope and (ii) intercept of the lines depends?
Answer:
The graph between variation of stopping potential and frequency is shown in Fig.
Since work function W = h0
Let W1 be the work function of photosensitive material A and W2 is that of B, then the threshold frequency for material A will be greater than that of B.
The slope of the line = V
i.e. the slope of the line is the ratio of stopping potential and frequency which is constant for all metals. The intercept of the line depends upon the threshold frequency and larger the work function, more will be the threshold frequency.
15. Using photon pictures of light, show how Einstein’s photoelectric equation can be established. Write two features of photoelectric effect which cannot be explained by wave theory.
Answer: Einstein’s photoelectric equation:
Radiation with frequency ν consists of a stream of discrete quanta or photons, with energy hν, where h is Planck’s constant. Photons travel at the speed of light through space.
When photons and electrons in the emitter’s atoms collide when radiation of frequency ν is incident on a photosensitive surface. During such a collision, the photon’s whole energy is transmitted to the electron with no time lag.
A photon is not a material particle but a quanta of energy. The incident photon’s absorbed energy hv by an electron is utilized in two ways. The electron uses some of its energy to break free from the atom. The minimum energy required to free-electron from a given surface is called the photoelectric work function φ0 of the material of the surface.
(i) Wave theory could not explain instantaneous emission of photons.
(ii) Wave theory could not explain the concept of threshold frequency.
16. Find the frequency of light which ejects electrons from a metal surface, fully stopped by a retarding potential of 3V. The photoelectric effect begins in this metal at a frequency of 6 x 1014 Hg. Find the work function for this metal (Given h = 6.63 x 10-34 Js)
Answer:
Here c = 1.6 x 10-19 C, V = 3V and v0 = 6 x 1014 Hz
From Einstein’s photoelectric equation
12 mv2= hv -W0
or eV0 = hv - hv0
or hv = eV0 + hv0
or v = eV0h + v0
= 1.610-1936.6310-34 + 6 x 1014
= 7.24 x 1014 + 6 x 1014 = 13.24 x 1014
or v = 1.324 x 1015 Hz.
17. What do you mean by "free electrons” in metals? Define work function.
Answer:
Free electrons in metals:
Within a solid piece of a substance like lithium, atoms are closely packed and, therefore, the loosely bound electrons of each atom are easily moved from the influence of their nucleus to that of their neighbor. Such loosely bound (actually unbounded) electrons are called free electrons.
Work function;
The minimum energy required in order to remove the electrons from the metal surface so as to overcome the surface barrier is called the work function of the metal.
It is measured in electron volt (eV). The work function of a metal depends upon its nature and condition of its surface.
18. What is the photoelectric effect? Give Experimental study of photoelectric effect .
Answer:
Photoelectric effect: In 1887, Hallwachs discovered that an insulated Zn-plate, negatively charged, lost its charge if exposed to ultraviolet light. Hertz had previously noticed that a spark passed more easily across the gap of an induction coil when the negative metal terminal was exposed to sun light. Afterwards, it was discovered that alkali metals like Li, Na, K, Rb and Cs eject electrons when illuminated by visible light. Thus, the surface atoms absorb the energy of radiation falling on them and emit electrons. This is called the photoelectric effect.
The phenomenon of ejection of electrons from a metal surface when illuminated by light, or any other radiation of suitable wavelength (or frequency) is called photoelectric effect. The emitted electrons are called photoelectrons because they are liberated by means of light.
Experimental study of photoelectric effect: Photoelectric phenomenon can be studied by a simple device as shown in Fig. It consists of a simple quartz tube T with a photosensitive plate P called emitting electrode and the other electrode C called collecting electrode. This tube with electrodes is called a photo tube. Ultraviolet light can be made to enter the tube through a window W.
A H.T. battery B is connected to a resistance R the mid point of which is earthed so that the plate P is at zero potential. Collector C can be maintained at a desired positive or negative potential w.r.t. P. The potential difference between the electrodes P and C can be measured by a voltmeter V and current flowing in the circuit by microammeter (µA).
In the absence of any radiation there is no flow of the electrons in the circuit and the microammeter shows no deflection. When ultraviolet light is made to fall on photosensitive plate P, it emits photoelectrons which are collected by the collecting plate C and the current flows in the circuit as indicated by the microammeter.
19. Why Classical Theory (i.e. Wave theory) fails to explain the phenomenon of photoelectric emission?
Answer:
Failure of Classical or Wave Theory:
Laws of photoelectric emission cannot be explained on the basis of the wave nature of light.
- On the basis of the nature of light it cannot be explained why light of high intensity but of frequency less than threshold frequency cannot produce photoelectric emission, whereas light of low intensity but higher frequency cannot produce photoelectric emission.
- It cannot explain the result that kinetic energy of emitted electrons is independent of intensity of incident light.
- Instantaneous emission of photoelectrons could not be explained by classical theory.
20. What is a photocell? Explain different types of photocells.
Answer:
Photocell or Photoelectric cell:
Photoelectric cell is a device for converting light energy into electrical energy. It is based on the photoelectric effect. Photoelectric cells are mainly of three types.
I. Photoemissive cell
II. Photovoltaic cell
III. Photoconductive cell
Photoemissive cell
Photoemissive cells are of two types:
(a) Vacuum type
(b) Gas filled type.
(а) Vacuum type Cell
Principle: Photoemissive is based on the principle that electrons are emitted from the cathode when illuminated by radiations of suitable frequency.
Construction: It consists of an evacuated glass bulb fitted with two metallic electrodes i.e. a cathode and an anode as shown in Fig. Cathode C is semi-cylindrical metal coated with photosensitive material and connected to the negative terminal of the battery B. Anode A is in the form of a straight wire so placed that it does not obstruct the light falling on cathode.
Working: When visible U.V. light is made to fall on the photosensitive cathode, electrons are emitted which are attracted by the positive anode. The magnitude of current is directly proportional to the intensity of incident radiations though the magnitude of current is small.
(b) Gas filled type cell: To increase the magnitude of the current the cell is filled with an inert gas like argon or neon. When cathode C is illuminated by radiations of suitable frequency, the emitted electrons from the cathode ionize the gas, hence a large number of electrons are produced. These electrons are attracted by the anode, so a large current is produced by this cell. In these cells, the magnitude of the photoelectric current is not proportional to the intensity of incident radiations.
Uses:
- They are used for sound reproduction from a motion-picture film.
- In television
- As burglar’s alarm.
- In photometry
- To control the temperature of furnaces.
21. Find the number of photons emitted per second by a 25W source of monochromatic light of wavelength 6000Å.
Answer:
Energy of photon
E = hv = hc=6.610-343108600010-10
= 3.3 x 10-19 J
So number of photons emitted per second by 25W source
n = 25W1s3.3 x 10-19 J
or n = 7.57 x 1019.
22. What are the important applications of photocell?
Answer: The photoelectric cells have been the following important applications:
1. Modern Talkies or Cinematography: In sound motion pictures or modern talkies, now so commonly used, a sound track is provided at the edges of the picture film.
2. Television: Television is the process of transmission and reproduction of moving figures at a distance and this method is similar in many respects to the transmission of pictures. In television, the pictures already contained on a photographic film are reproduced, while in transmission of pictures an actual moving figure, say the face of the actor, is reproduced. The process of television involves the following essential points:
- Scanning of the object which is to be televised. It consists in dissecting the object into a large number of elements by making a narrow and intense beam of light more rapidly back and forth over a limited portion of the object.
- Conversion of light impulses received from the scanned object into electric impulses, for which the photoelectric cell is used.
- Reconversion of the electric impulses back to light impulses in such a way as to reconstruct the original object. The first two points are attended to by a television transmitter while the third by a television receiver.
3. Burglar Alarm: Infrared light is invisible to the eye. When a beam of infrared light is projected across the room in which a photoelectric cell is fitted in a closed circuit. When the burglar walks in that room he cuts the incident light and stops the photoelectric current momentarily. This actuates an electric relay which causes another electric circuit to be completed, thereby ringing the bell.
In the above case, the photoelectric cell is continuously working. In another arrangement i.e. in the open circuit the cell is actuated only when another source of light e.g. the light of the intruder torch, when the photoelectric current produced actuates a relay which closes the electric bell circuit, thereby ringing the bell.
4. Micro photometers: These are the instruments for measuring the intensity of light and studying the final structure of a spectral line. These use photoelectric cells.
5. Fire Alarms: To protect a building from fire, gas filled photoelectric cells are used at various places in the building. Whenever there is a flame, the fight falls on the cell and photoelectric current is produced which after suitable amplification causes a bell to ring.
6. Counting Machines: An important example of counting machines is met with on docks where it is used to count the number of packages or bags loaded in a ship. A beam of fight falls on a photoelectric cell (gas filled) and the current after amplification starts a counting machine. As soon as the path of the beam is cut off by the package, the current stops for a while and the counting machine advances by one.
7. Automatic Switching of Street Lighting Circuit: A photoelectric cell is also used in the street lighting circuit. The sunlight falls on it and the current generated keeps the circuit open. As soon as the intensity of sunlight falls below a certain value (e.g. in the evening) the photoelectric current becomes very feeble and the street light circuit is closed. This method has the advantage that the time of street light is automatically adjusted in summer and winter.
8. Exposure Meters in Photographs: An exposure meter is a device to calculate the correct time of exposure. The photoelectric cell in the instrument produces a current proportional to the intensity of light falling on it. The current operates a galvanometer, the scale of which is calibrated to read the time of exposure.
9. Complexion Meters: The light reflected from the face of a person falls on a photoelectric cell when the current produced is proportional to the intensity of the reflected light and such measures the complexion of the person.
10. Daylight Recorders: Photoelectric cells find use in meteorology to record daylight. The current produced in a photoelectric cell with daylight is coupled with a clock system and a current time graph is plotted giving a measure of daylight.
11. These cells are also used in traffic signals, color identification etc.
23. Radiation of wavelength 5000Å and of intensity 2 x 10-3 w cm-2 falls on a photosensitive surface. Assuming that every absorbed photon results in the ejection of photoelectron, find how many photoelectrons are produced per cm2 per sec.
Answer:
Here I = 2 x 10-3 W cm-2, λ = 5000Å = 5 x 10-7 m
Energy of one photon
E = hv = hc
Or E = 6.6210-343108510-7 = 4 x 10-19J
Number of photons incident per unit area per sec.
n = IE=210-3410-19
= 5 x 1015
24. What is the physical meaning of a wave packet?
Answer: Wave packet:
The de-Broglie wave associated with a material particle has velocity more than the velocity of the particle. So it was difficult to conceive as to how the de-Broglie wave was associated with the particle. Schrodinger postulated that a moving particle is not associated with one wave but a group of waves called wave-packet; and each wave has slightly different speed and wavelength. The wave packet is the result of a superposition of individual waves whose interference with one another results in the variation of amplitude that defines the group shape. Since the wave speed varies with wavelength, hence the different individual waves do not proceed together and the wave packet has speed different from that of the waves which compose it. The amplitude of each wave is so chosen that they interfere constructively over a small region of space as shown in Fig. LAQ 11. The velocity of a wave packet when calculated comes out to be equal to the velocity of the material particle with which it is associated.
Thus a wave packet is a type of wave motion in which the amplitude of the wave is very large in a small region and negligibly small in the rest of space. The probability of finding the particle is maximum, where amplitude of the waves is large and probability is minimum where amplitude of the wave is small.
25. Describe an experiment which shows the wave nature of electrons.
Or
Describe experimental verification of de-Broglie wave equation.
Answer: Davisson and Germer Experiment: The first experimental proof of the wave nature of particles was proved in 1927 by C.J. Davisson and L.H. Germer.
Principle: Electrons accelerated by a known potential are diffracted from a crystal and their wavelength is measured by optical formula.
Construction: The experimental arrangement used by Davisson and Germer is as shown in Fig. The electrons from a hot tungsten cathode are accelerated by a potential difference V between the cathode C and anode A. This arrangement is called an electron gun. A Ni crystal is placed such that the electrons strike on it at an angle O. The detector D can move along an arc scale with its center O as shown in the figure.
Working. A fine beam of electrons is allowed to strike the Ni target. The intensity of scattered electrons in a given direction is determined by a detector. The intensity of scattered beam is measured at different values osf Φ and a graph is plotted between Φ and intensity of scattered beam. Such graphs are plotted at different accelerating voltages as shown
Fig. From these graphs we find that the scattered electron beam of 54 V has diffraction peak at angle Φ = 50°. This appearance of bump at a particular direction is due to the interference of electrons scattered from different layers of regularly spaced atoms of the crystal. This established wave nature of electrons.
It is found that the maxima in the diffraction pattern occurs, when Bragg's condition is satisfied. i.e. 2d sin θ = nλ .......................(1)
where d is the distance between atomic planes, λ is the wavelength of the electron and n is the order of spectrum.
From the we have
θ + Φ + 0 = 180°
∴ 2 θ = 180° - Φ = 180° - 50°
= 130°
∴ θ = 65°
For n = 1, Eq. (1) becomes
λ = 2 d sin θ
For Ni crystal d = 0.91 Å = 0.91 x 10-10m
∴ λ= 2 x 0.91 x 10-10x sin 65°
λ = 1.65 Å
Also for 54 V, the de-Broglie wavelength of electron is given by (theoretically)
λ = 12.2754 Å = 1.67 Å
Thus the two results are in close agreement with each other. So Davisson and Germer experiment provides direct verification of de-Broglie hypothesis of wave nature of moving particles.
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