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The dual nature of radiation and matter tells us that every object has two natures associated with it i.e. radiation and matter.
- According to classical physics, the whole universe is made of two things i.e. radiation and matter.
- They are independent of each other and both have separate unique properties.
- Matter has momentum (mass and velocity) and radiation has wavelength and frequency.
- After 1900, it was found that matter has the properties of radiation, and radiation has the properties of matter.
- It was found that when a metal is exposed to ultra-violet light emissions of electrons take place.
- It shows that UV rays have momentum when they strike metal surfaces, resulting in the emission of electrons from the metal.
- Therefore, electromagnetic radiation exhibits both properties.
Key Terms: Matter, Radiation, Photoelectric Effect, Dual nature of radiation and matter, Kinetic energy, Threshold frequency, de-Broglie’s wavelength, Waves, Einstein’s photoelectric equation
Electron Emission
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The process of emission of electrons from a metal surface is called electron emission.
- Metals contain both electrons and protons.
- Electrons are bound inside the metal due to the attractive forces.
- As the electrons tend to leave the metal, a positive charge is developed and pulls back the electrons.
- This attractive force acts like a surface barrier of electrons.
- With the help of external energy, electrons can release themselves from the metal.
- The minimum requirement of energy to pull the electron from the metal is called the work function of the metal.
Certain methods lead to the emission of electrons from the metal surface. These methods are discussed below:
Photo-electric emission
It is the process of emission of electrons when light of suitable frequency is incident on a metal surface.
Photo-electric emission
Field emission
It is the process of emission of electrons when a strong electric field is applied across the metal surface. It is also known as cold emission or cold cathode emission.
Field Emission
Thermionic emission
It is the process of emission of electrons when a metal is heated.
Thermionic Emission
| Solved Examples of Electron Emission Ques. Two photons, each of energy 2.5eV are simultaneously incident on the metal surface. If the work function of the metal is 4.5eV, then from the surface of the metal. How many electrons will be emitted? Ans. Not even a single electron will be emitted. Since the energy of each photon (2.5 eV) is lesser than the work function (4.5 eV), there will not be any emission of electrons. The photons will be absorbed and will excite the electrons. But the electrons will still remain bound to the metal. Ques. In which type of electron emission, do the electrons use high-speed electrons to emit from the surface? Ans. The minimum energy required by an electron to just escape (i.e. with zero velocity) from the metal's surface is called the Work function (W0) of the metal. There are four methods of producing electron emission,
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Photoelectric Effect
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The photoelectric effect is the phenomenon of emission of electrons from metal surfaces exposed to light energy of suitable frequency.
- When light energy of a specific frequency strikes the metal surface, the energy of the light is shared by the free electrons of the metal.
- This causes electrons to be released from the metal surface instead of the attractive forces of protons.
- Due to the photoelectric effect, light energy gets converted into electrical energy, and the current produced due to the photoelectric effect is called photoelectric current.
Hertz and Lenard’s Observations of the Photoelectric Effect
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The emerging topic of photoelectricity attracted the scientific world in the late 19th and early 20th centuries.
- The phenomena of releasing electrons from a metal surface contradicted traditional physics and opened the path for quantum mechanics.
- Heinrich Hertz and Philipp Lenard were major contributors to solving its mysteries.
Hertz Observations
In 1887, Heinrich Hertz experimented to investigate the production of electromagnetic waves using spark discharge.
- He used a detector made of wire bent in a circle with metallic spheres.
- The electromagnetic radiation produced by the induction coil falling on the detector induced potential differences across the gap of the spheres.
- Hertz observed that sparks across the gap jumped more rapidly when the detector was exposed to UV light.
- This observation led him to conclude that light helps the emission of electrons from the metallic spheres.
Hertz Observation
Lenard Observation
Philipp Lenard used the apparatus consisting of a highly evacuated tube having two electrodes i.e. cathode and anode.
- He observed that when UV light was incident on metallic electrodes, an electric current appeared in the circuit.
- He concluded that only light of suitable frequency called threshold frequency results in photoelectric current.
- This experiment is also known as the experimental study of the photoelectric effect.
Factors Affecting the Photoelectric Effect
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Certain factors determine the photoelectric effect and in turn, also determine the photoelectric current. Let's discuss each of the factors in depth:
Light Intensity
It is a well-known fact that the photoelectric current depends on the number of electrons escaping the metal surface in one second.- This indicates that the photoelectric current is in direct relation to the intensity of the light.
- So, the graph between photoelectric current and light intensity will be a straight line.
Light Intensity
Potential
Stopping potential is the minimum provided on the metal plate that stops the photoelectric current.
- The minimum negative potential is the retarding potential as it is retarding the photoelectric current.
- The Kinetic Energy of the photoelectrons doesn’t depend on the intensity of the incident light.
Potential
Effect of frequency on the stopping potential
The frequency of incident light is directly proportional to the maximum kinetic energy of the electrons.
- This indicates that there will be a greater requirement of retarding potential to stop the electrons from emitting out of the metal plate.
- Two important graphs to represent the same are given below:
Effect of frequency on the stopping potential
| Solved Example of Photoelectric Effect Ques. A radiation of wavelength 300 nm is incident on a silver surface. Will photoelectrons be observed? Ans. The energy of the incident photon is E = hv = hc/λ (in joules) E = hc/λe (in eV) Substituting the known values, we get E = 6.626×10−34 ×3×108 / 300×10−9 ×1.6×10−19 E = 4.14 eV Since the energy of the incident photon is less than the work function of silver, photoelectrons are not observed in this case. |
Read Also:- Nature of Light
Laws of Photoelectric Emission
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The following are the laws of photoelectric emission
- Whatever the intensity of incident light, there is a minimum frequency of incident light termed threshold frequency below which no photoelectric emission occurs for a particular photosensitive material.
- If the frequency of incident light is larger than the threshold frequency, the number of photoelectrons released per second, i.e. photoelectric current, is directly proportional to the intensity of the light.
- The photoelectric emission process is instantaneous. The time lag between photoelectron generation and radiation incidence is almost equivalent to 10-9 s.
- The maximal kinetic energy of photoelectrons increases as the frequency of incident light increases, provided the frequency of incident light is larger than the threshold frequency.
Einstein's Photoelectric Equation
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Einstein proposed a theory in 1905 based on Planck’s hypothesis of quanta to explain the photoelectric effect.
Einstein's photoelectric equation is given by
\(\frac{1}{2}mv^2=h(f-f_o)\)
Where
- 1/2 mv2 is the kinetic energy of the photoelectrons.
- h is the Planck’s constant
- f is the frequency of the incident light
- fo is the threshold frequency
Photons
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A photon is a packet of energy or quantum of energy ejected at the speed of light by an emitter. The energy of each packet of photon is given by
\(E=hf\)
Where
- h is the Planck’s constant
- f is the frequency of the incident light
Properties of Photons
The following are the properties of photons
- A photon travels with the speed of light in a vacuum.
- A photon has no mass or charge, and it is not reflected in a magnetic or electric field.
- During the interaction of matter with radiation, radiation behaves as it is made up of small particles called photons.
- Photons are hypothetical particles.
- The energy of a photon is proportional to its frequency but inversely proportional to its wavelength.
- The wavelength of photons changes in different media, therefore the velocity of photons is different in different media.
Expression for de-Broglie Wavelength
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The waves associated with moving material particles are known as de-Broglie waves or matter waves.
According to de-Broglie, the wavelength of the waves associated with a material particle is given by
\(\lambda=\frac{h}{p}=\frac{h}{mv}\)
Where
- λ is the wavelength of the wave
- h is Planck’s constant
- p is the momentum of the particle
Terminologies Related to the Dual Nature of Matter and Radiation
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The following are the basic terms related to the dual nature of matter and radiation
- Free electrons are those which can freely move inside the metal plate but can’t escape the metal surface.
- Electron emission takes place when sufficient energy is provided to the metal surface which leads valence electrons to escape the metal plate and move in the surrounding space.
- Work Function is the minimum requirement of energy that helps to eject the electrons from the surface of the metal. The electron will keep on moving inside the metal though it has left its valence shell.
- The threshold frequency is the minimum frequency of light that can emit electrons from the metal surface.
Previous Year Questions
- A photocell stops emission if it is maintained at 2 V positive potential… [JIPMER 1999]
- Two fast moving particles X and Y are associated with de Broglie… [KEAM 2013]
- The activity of ratio altitude (X100) is 6.023 curie… [AP EAPCET 1998]
- If the Planck’s constant h=6.6×10−34Js, the de Broglie wavelength… [BITSAT 2018]
- An electron is accelerated under a potential difference of 182 V… [BITSAT 2011]
- In the ideal double-slit experiment, when a glass-plate… [JEE Advanced 2002]
- An example for the best source of monochromatic light is… [JKCET 2019]
- An electron of mass m is accelerated by a potential difference V... [WBJEE 2016]
- The kinetic energy of an electron get tripled then the… [VITEEE 2012]
- A direct X-ray photograph of the intenstines is not generally taken by… [VITEEE 2012]
- A 200W sodium street lamp emits yellow light of wavelength… [NEET 2012]
- Light with an average flux of 20Ω/cm2 falls on a non-reflecting surface at… [NEET 2020]
- A 5 watt source emits monochromatic light of wavelength… [NEET 2007]
- When the light of frequency 2v0 (where v0 is threshold frequency), is… [NEET 2018]
- An electron of mass m with an initial velocity… [NEET 2018]
- A beam of cathode rays is subjected to crossed electric… [NEET 2010]
- A beam of electron passes undeflected through mutually perpendicular… [NEET 2007]
- When light of wavelength 300 nm (nanometer) falls on a photoelectric emitter… [NEET 1993]
- The de-Broglie wavelength of a neutron in thermal equilibrium… [NEET 2017]
- A particle of mass 1 mg has the same wavelength as an electron moving… [NEET 2008]
Thing to Remember
- A matter can possess or display wave nature (exhibiting the phenomenon of interference and diffraction) and particle nature (quanta/packets of light).
- Metals contain both electrons and protons.
- Electrons are bound inside the metal due to the attractive forces but with the help of energy, electrons can release themselves from the metal.
- Certain methods lead to the emission of electrons from the metal surface.
- These methods are Photo-electric Emission, Field Emission, and Thermionic Emission.
- The photoelectric effect is the scientific phenomenon in which electromagnetic radiation occurs on the metal surface.
- Due to the photoelectric effect, light energy gets converted into electrical energy, and the current produced due to the photoelectric effect is called photoelectric current.
Sample Questions
Ques. A proton and an electron have equal speeds. Obtain the ratio of de Broglie wavelengths associated with them. (2 Marks)
Ans. \(\lambda = \frac{h}{mv} \)
\(\frac{\lambda_p}{\lambda_e} = \frac{m_e}{m_p} = \frac{1}{1836}\)
Ques. Define the term “intensity” in a photon picture of electromagnetic radiation. (2 Marks)
Ans. Electromagnetic radiation is a form of energy that is present around us invisibly. For instance, X-rays, radio waves, microwaves, and so on. The intensity of electromagnetic radiation refers to the number of photons that pass through a given space.
Ques. Two protons of equal kinetic energies enter an area of equal magnetic field. The first proton enters normal to the field direction whereas the second enters at 30 degrees to the field direction. What are the trajectories followed by them? (3 Marks)
Ans. As we know when a charged particle enters a uniform magnetic field, the force expended on it is,
F = q(v x B) = qvb sinθ
In case 1, when the particle enters perpendicular, θ= 90
Here the particles start moving in a circular path with radius as sinθ = 1 is the maximum value.
In case 2 where a particle enters at an angle of 30 degrees, the force acting on it has two components. Thus, due to the resultant of the two components, the particle will move along a helical path.
Ques. Write one reason to explain why the wave theory of light does not support the photoelectric effect. (2 Marks)
Ans. One of the reasons why the wave theory of light does not support the photoelectric effect is that the kinetic energy of photoelectrons does not depend on the intensity of the incident light. Moreover, according to the wave theory, after the light falls on a substance, the electrons are emitted after a certain period of time. However, in the photoelectric effect, electron emissions are immediate without a time delay.
Ques. Plot a graph that shows the variation of de Broglie wavelength λ associated with a charged particle mass m, versus 1/√V where V is the potential difference through which the particle is accelerated. In which way does this graph give information regarding the magnitude of the charge of the particle? (5 Marks)
Ans. Let us assume a particle of charge q and mass m
To gain speed V and kinetic energy KE, let it be accelerated by a potential difference v
Therefore,
\(KE = qV = \frac{1}{2}mv^2\)
Now, by rearranging the expression we get,
\(v = \sqrt{\frac{2qV}{m}}\)
The de Broglie wavelength equation,
\(\lambda = \frac{h}{mv}\)
Substituting the value v we get,
\(\lambda = \frac{h}{\sqrt{2mqV}}\)
We already know the equation of the straight line,
Y = mx where m is the shape of the line.
Thus, on plotting the graph of versus \(\frac{1}{\sqrt{V}}\)
We will have a straight line with a slope.
\(S = \frac{h}{\sqrt{2mq}}\)
Rearranging we get,
\(q = \frac{h^2}{2mS^2}\)
The graph of λ verses
Therefore, we can determine S from the graph which lends us information regarding the magnitude of the charge of the particle.
Ques. Monochromatic light of frequency 6.0 X 1014 Hz is produced by a laser. The power emitted is 2.0 X 10-3 W . Then calculate the (i) energy of photons in the light beam and (ii) the number of photons that are emitted on average by the source. (3 Marks)
Ans. (i) Energy of photon = hv
\(=6.63 \times 10^{-34} \times 6 \times 10^{14} J\)
\(= 3.978 \times 10^{-19} J\)
Number of photons emitted per second = (Power / Energy of Photon )
\(= \frac{2 \times 10^{-3}}{3.978 \times 10^{-19}} = 5.03 \times 10^{-15} Photon/sec\)
Ques. Write two properties of photons. For a monochromatic radiation incident on a photosensitive surface, why all photoelectrons do not come out with the same energy? Give a reason for your answer. (3 Marks)
Ans. The two properties of photons are as follows:-
The photons are electrically neutral
Photon has an energy that is equivalent to hv.
For a monochromatic radiation incident on a photosensitive surface, all photoelectrons do not come out with equal energy as in addition to the work done to the free electrons from the surface, different emitted photoelectrons require different amounts of work to be done on them to reach the surface.
Ques. Draw a graph showing the variation of stopping potential with frequency of incident radiations for two photosensitive materials A and B having threshold frequency VA > VB.
(i) In which case the stopping potential will be more and why?
(ii)Does the slope of the graph depend on the nature of the material that is used? Explain. (3 Marks)
Ans.
(i) For material B, because for the same value of ‘v’, the stopping potential is more for material B.
Therefore, V0 is higher for the lower value of v0
(ii) No, the slope of the graph does not depend on the nature of the material used as the slope is given by h/e which is constant.
Ques. (a) State three observed features of the photoelectric effect that can not be explained by the wave theory of light. Explain how Einstein’s photoelectric equation is used to describe these features.
(b) The figure shows a plot of stopping potential V0 with frequency v of incident radiation for two photosensitive materials M1 and M2.
Answer the following questions:
(i) Why is the slope of both the lines the same?
(ii) for which material emitted electrons have greater kinetic energy for the same frequency of the incident radiation? (5 Marks)
Ans. (a) The three observed features are as follows,
The maximum kinetic energy of the electrons that are emitted should be directly proportional to the intensity of incident radiations but it is not observed experimentally. Also, the maximum kinetic energy of the emitted electrons should not depend upon incident frequency based on the wave theory, but it is not so.
According to the wave theory, the threshold frequency should not be present. Light of all frequencies should emit electrons where the intensity of light is sufficient for the electrons to eject.
Based on the wave theory, the photoelectric effect should not be instantaneous. Wave energy can not be transferred to a particular electron but will be distributed to all the electrons present in the illuminated portion. Therefore, there must be a time lag between the incidence of radiation and the emission of electrons.
(b) (i) The slope (V0/v) of both the lines is the same which represents the universal constant known as Planck’s constant (h) = 6.62 x 10-34 JS
(ii) For the same frequency of incident radiations, M1 will have greater kinetic energy as the value of V0 is greater for M1 material. It can be easily observed by drawing a vertical line, the frequency being the same and intersecting M1 and M2 at different points.
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