WAVE +PARTICLE =WAVICLES

The Phenomenon explaining particle nature of light.

 BECAUSE METALS HAVE FREE ELECTRONS.

 NO

 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.

 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.)

 The energy required to take out electron from the metal surface.

 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.

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.

 Intensity of incident light –  On increasing the intensity of incident light photoelectric current increased. 

 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.

 i.e. K max = eV 0 ( v =w/q)  Here V 0 is 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

 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.

 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

 where E represents energy on y axis  ν represents frequency on x axis.  B is the intercept of the graph on y axis.

 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.

 There is no time lag between the incidence of photons & emission of electrons.

 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.

Quantum theory is a theory needed to describe physics on a microscopic 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

 Quantum theory describes light as a particle called a photon  According to quantum theory, a photon has an energy given by E = h = hc/ h = 6.6x [J s] Planck’s constant, 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.

 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 =hν 0

 Thus  hν = hν 0 + 1/2mv 2  1/2mv2 = h( ν - ν 0 )  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 < ν 0 then K.E. will be negative i.e. impossible,hence emission of electrons below threshold frequency is not possible.

 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.

 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.

 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 by E = hc/, where h = Planck’s constant = 6.6x [J s] and, c = speed of light = 3x10 8 [m/s] = wavelength of the light (in [m])  Photons also carry momentum. The momentum is related to the energy by: p = E / c = h/  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 by E = hc/, where h = Planck’s constant = 6.6x [J s] and, c = speed of light = 3x10 8 [m/s] = wavelength of the light (in [m])  Photons also carry momentum. The momentum is related to the energy by: p = E / c = h/

On macroscopic scales, we can treat a large number of photons as a wave. When dealing with subatomic phenomenon, we are often dealing with a single photon, or a few. In this case, you cannot use the wave description of light. It doesn’t work !

 De Broglie generalized the idea of dual nature of radiation to matter.

 Wave (electromagnetic) - Interference - Diffraction  Particle (photons) - Photoelectric effect - Compton effect Wave - Particle Duality for light

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!

The dual nature of matter A particle with momentum p has a matter wave associated with it, whose wavelength is given by

Dual Nature Radiation Matter

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!

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

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

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

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

If several waves of different wavelengths (frequencies) and phases are superposed together, one would get a resultant which is a localized wave packet

 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!

 A wave packet 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!

Uncertainty in Position : Uncertainty in Momentum:

If is large, is small

 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

 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

 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

 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

 Observations: ◦ Intensity was stronger for certain angles for specific accelerating voltages (i.e. for specific electron energies) ◦ Electrons were reflected in almost the same way that X- rays of comparable wavelength

 Observations: ◦ Current vs accelerating voltage has a maximum, i.e. the highest number of electrons is scattered in a specific direction ◦ This can’t be explained by particle-like nature of electrons  electrons scattered on crystals behave as waves For φ ~ 50° the maximum is at ~54V

 For X-ray Diffraction on Nickel

 (Problem 40.38) Assuming the wave nature of electrons we can use de Broglie’s approach to calculate wavelengths of a matter wave corresponding to electrons in this experiment  V = 54 V  E = 54 eV = 8.64× J This is in excellent agreement with wavelengths of X-rays diffracted from Nickel!

 In previous experiments many electrons were diffracted  Will one get the same result for a single electron?  Such experiment was performed in 1949 ◦ Intensity of the electron beam was so low that only one electron at a time “collided” with metal ◦ Still diffraction pattern, and not diffuse scattering, was observed, confirming that Thus individual electrons behave as waves