DUAL NATURE OF MATTER AND RADIATION

1. DUAL NATURE OF MATTER AND RADIATION WAVE +PARTICLE =WAVICLES

2. PHOTOELECTRIC EFFECT The Phenomenon explaining particle nature of light.

3. EMISSION OF ELECTRONS FROM METALS, WHY? • BECAUSE METALS HAVE FREE ELECTRONS.

4. Do these free electrons are so free as to come out of the metal on their own? • NO

5. WHY? • Because these electrons are strongly attracted by the group of positive ions inside. • It is remarkable that these positive ions are formed only when the electrons of the outermost orbit(now free electrons) leave the atom. • Hence some energy is required to take out these so called free electrons • On this basis(source of energy) electron emission is of following types.

6. TYPES OF ELECTRON EMISSION • THERMIONIC EMISSION • Emission of electrons by heat energy. • ELECTRIC FIELD EMISSION • – Emission of electrons by applying electric field. • PHOTOELECTRIC EMISSION – • Emission of electrons due to photons(i.e. light of suitable frequency.)

7. WORK FUNCTION φ • The energy required to take out electron from the metal surface.

8. PHOTOELECTRIC EMISSION

9. The wavy lines represent light. • Thus incidence of light of suitable frequency on a metal surface causes the emission of electrons. The phenomenon is known as photoelectric emission & the electrons are known as photoelectrons. If these electrons are directed in such a way so as to obtain current then this is known as photoelectric current.

10. Experimental set up-

11. Incident light triggers the emission of (photo)electrons from the cathode • Some of them travel toward the collector (anode) with an initial kinetic energy • The applied voltage V either accelerates (if positive) or decelerates (if negative) the incoming electrons. • The intensity I of the current measured by the ammeter as a function of the applied voltage V is a measurement of the photoelectron properties, and therefore a measurement of the properties of the photoelectric effect.

12. Observations of Lenard & Millikan- • Intensity of incident light – • On increasing the intensity of incident light photoelectric current increased.

13. Photoelectric current α Intensity of incident light.

14. Potential applied at the collector- • For the potential increased from zero to some positive value the photoelectric current increased as it attracted more & more electrons. • For negative potential i.e. Retarding potential applied on the collector the photoelectric current decreased gradually. • At a certain value of negative potential the photoelectric current became zero. This is called as Stopping or Cut off potential.

15. This stopping potential is a measure of maximum K.E. of electrons. • i.e. Kmax = eV0 ( v =w/q) • Here V0 is stopping potential.

16. Effect of Intensity at Stopping Potential- • At the stopping potential when intensity was increased no current was obtained. • This implies that increasing intensity does not give so much courage (energy) to the electrons so as to overcome the barrier posed by retarding potential i.e. to say • Intensity is not related to energy

17. Effect of frequency of light- • At the stopping potential when frequency of light was increased current was obtained. • This implies that frequency must have increased the energy of electrons. • On studying the variation between frequency of incident light & K.E. of emitted electrons the following graph was obtained.

18. Frequency vs Retarding Potential i.e. a measure of max. K.E.

19. Conclusions from graph • For every metal there exists a certain frequency below which emission of electrons cannot occur known as threshold frequency. • At this frequency the K.E. of emitted electrons is zero. • The graph for different metals are parallel straight lines implying that the slope of the graph must be a universal constant. • Taking analogy of the equation – y = mx+c • Equation of straight line in the graph can be

20. E = Aν-B • where E represents energy on y axis • ν represents frequency on x axis. • B is the intercept of the graph on y axis.

21. Laws of Photoelectric Emission • The no. of photoelectrons emitted is directly proportional to the intensity of incident light. • The energy of photoelectrons does not depend upon intensity of light. • The energy of electrons is directly proportional to the frequency of incident light. • There exists a certain minimum frequency below which electron emission does not occur known as threshold frequency.

22. Laws Contd. • There is no time lag between the incidence of photons & emission of electrons.

23. Failure of wave theory • The intensity of the radiation should have a proportional relationship with the resulting maximum kinetic energy. • The photoelectric effect should occur for any light, regardless of frequency or wavelength. • There should be a delay on the order of seconds between the radiation’s contact with the metal and the initial release of photoelectrons.

24. What is Quantum Theory? Quantum theory is a theory needed to describe physics on amicroscopic scale, such as on the scale of atoms, molecules,electrons, protons, etc.Classical theories: Newton – Mechanical motion of objects (F = ma) Maxwell – Light treated as a wave Quantum (from Merriam-Webster) Any of the very small increments or parcels into which many forms of energy are subdivided. Light is a form of energy is a quantum of EM energy

25. Photons • Quantum theory describes light as a particle called a photon • According to quantum theory, a photon has an energy given byE = hn = hc/lh = 6.6x10-34 [J s]Planck’sconstant, after the scientist Max Planck. • The energy of the light is proportional to the frequency (inversely proportional to the wavelength) ! The higher the frequency (lower wavelength) the higher the energy of the photon.

26. Einstein’s explanation- • A photon’s energy(hν) is used in two ways- • Energy required to take the electron out of the metal surface(work function W) • Energy left is the K.E. of the electron emitted. • Mathematically- • hν = W + K.E. • Here W represents the minimum energy required to take out electron from the metal surface. Hence from quantum theory • W =hν0

27. Where ν0 represents threshold frequency. • Thus • hν = hν0 + 1/2mv2 • 1/2mv2 = h(ν - ν0 ) • This is Einstein’s Photoelectric equation. • On the basis of this equation the laws of photoelectric emission can be explained- • As it is clear from the above equation energy of electrons emitted depends upon the frequency of incident light & not upon intensity. • If ν < ν0 then K.E. will be negative i.e. impossible,hence emission of electrons below threshold frequency is not possible.

28. How does this explain the photoelectric effect? • Think about hitting a ball into outer space. • If you don't hit it hard enough, it will just come back down. No matter how many times you hit it. • If superman hit it, he could get it into space. • Similarly, no matter how many photons strike the metal, if none of them has sufficient energy to eject an electron from a metal atom, you won't get a current. • If the energy the taken up by the electron is sufficient to allow it to be released from the metal atom, you will get a current.

29. Exp Contd. • Also photoelectric emission is an instantaneous phenomenon. The moment light is made incident on metal surface , photon is absorbed by the electron & it comes out. Hence there is no time lag.

30. Summary of Photons • Photons can be treated as “packets of light” which behave as a particle. • To describe interactions of light with matter, one generally has to appeal to the particle (quantum) description of light. • A single photon has an energy given byE = hc/l, where h = Planck’s constant = 6.6x10-34 [J s] and, c = speed of light = 3x108 [m/s]l = wavelength of the light (in [m]) • Photons also carry momentum. The momentum is related to the energy by: p = E / c = h/l

31. So is light a wave or a particle ? On macroscopic scales, we can treat a large number of photonsas a wave. When dealing with subatomic phenomenon, we are often dealingwith a single photon, or a few. In this case, you cannot usethe wave description of light. It doesn’t work !

32. Dual nature of matter • De Broglie generalized the idea of dual nature of radiation to matter.

33. Light has a dual nature___________________________ • Wave (electromagnetic) - Interference - Diffraction • Particle (photons) - Photoelectric effect - Compton effect Wave - Particle Duality for light

34. What about Matter?_______________________________ If light, which was traditionally understood as a wave also turns out to have a particle nature, might matter, which is traditionally understood as particles, also have a wave nature? Yes!

35. Louis de Broglie’s hypothesis____________________________ The dual nature of matter A particle with momentum phas a matter wave associated with it, whose wavelength is given by

36. The connecting link – Planck’s constant_______________________________ Dual Nature Radiation Matter

37. Why isn’t the wave nature of matter more apparent to us…?___________________________________ Planck’s constant is so small that we don’t observe the wave behaviour of ordinary objects – their de Broglie wavelengths could be many orders of magnitude smaller than the size of a nucleus!

38. Particle______________________________ Our traditional understanding of a particle… “Localized” - definite position, momentum, confined in space

39. Wave____________________________ Our traditional understanding of a wave…. “de-localized” – spread out in space and time

40. How do we associate a wave nature to a particle?___________________________________ What could represent both wave and particle? • Find a description of a particle which is consistent with our notion of both particles and waves…… • Fits the “wave” description • “Localized” in space

41. ____________________________________ A “Wave Packet” How do you construct a wave packet?

42. Constructing a wave packet by adding up several waves …………___________________________________ If several waves of different wavelengths (frequencies) and phases are superposed together, one would get a resultant which is a localized wave packet

43. Heisenberg's Uncertainty Principle___________________________________ • The Uncertainty Principle is an important consequence of the wave-particle duality of matter and radiation and is inherent to the quantum description of nature • Simply stated, it is impossible to know both the exact position and the exact momentum of an object simultaneously A fact of Nature!

44. A wave packet describes a particle____________________________ • A wavepacket is a group of waves with slightly different wavelengths interfering with one another in a way that the amplitude of the group (envelope) is non-zero only in the neighbourhood of the particle • A wave packet is localized – a good representation for a particle!

45. Heisenberg's Uncertainty Principle__________________________________ Uncertainty in Position : Uncertainty in Momentum:

46. Uncertainty Principle and the Wave Packet___________________________________ If is large, is small

47. Summary___________________________________ • Matter and radiation have a dual nature – of both wave and particle • The matter wave associated with a particle has a de Broglie wavelength given by

48. Davisson-Germer Experiment • If particles have a wave nature, then under appropriate conditions, they should exhibit diffraction • Davisson and Germer measured the wavelength of electrons • This provided experimental confirmation of the matter waves proposed by de Broglie

49. Davisson and Germer Experiment • Electrons were directed onto nickel crystals • Accelerating voltage is used to control electron energy: E = |e|V • The scattering angle and intensity (electron current) are detected • φ is the scattering angle

50. Davisson and Germer Experiment • If electrons are “just” particles, we expect a smooth monotonic dependence of scattered intensity on angle and voltage because only elastic collisions are involved • Diffraction pattern similar to X-rays would be observed if electrons behave as waves