Dual Nature of Matter and Radiation Notes PDF

# Dual Nature of matter and Radiation chapter-11 In some phenomenon like interference, diffraction, light behave like wave but in phenomenon like photo electric effect, light behave like particle. This proves that light/Radiation dual Nature. ## Work function It is the minimum amount of energy re...

# Dual Nature of matter and Radiation chapter-11 In some phenomenon like interference, diffraction, light behave like wave but in phenomenon like photo electric effect, light behave like particle. This proves that light/Radiation dual Nature. ## Work function It is the minimum amount of energy required by electrons to just leave the metal surface. It is denoted by *work function*. It is the smallest unit of energy. 1ev is the energy gained by electron on applying one volt potential difference. -19 Jev = 1.6 X10 J | Metal | Work function | |---|---| | Cs | 2.14 ev | | Al | 4.28 ev | | K | 2.30 ev | | H₂ | 4.49 ev | | Na | 3.75 ev | ## Electron Emission The phenomenon of ejecting electron from metal surface on providing it sufficient energy is called emission of electron. There are four methods of electron emission: 1. Thermionic Emission 2. Photoelectric Emission 3. Secondary Emission 4. Field Emission ## Hallwach & Lenard Experiment of photoelectric effect - The phenomenon of photoelectric emission was discovered in 1887 by Heinrich Hertz (1857-1894) during his electromagnetic wave experiments. - Wilhelm Hallwachs and Lenard investigated the phenomenon of photo electric emission in detail during 1886-1902. - Lenard observed that when ultraviolet radiations were allowed to fall on the emitter plate of an evacuated glass tube, current flows in the circuit. As soon as the UV radiation were stopped, the current flow also stopped. These observations indicate that ultraviolet radiations fall on the emitter plate C, electrons are ejected from it which are attracted towards the positive, collector plate A by the electric field. ## Laws of photo electric effect 1. There is no time lag between incident radiation and emission of electron. 2. Kinetic energy of photoelectrons depends on frequency of incident radiation. 3. Number of electrons emitted per second (photo electric current) depends on intensity of radiation. 4. There is a certain frequency below which electrons cannot be emitted from metal. This frequency is called threshold frequency. (ν_o) ## Graph between frequency of incident radiation and kinetic energy of photoelectron - K increases linearly with ν - For ν < ν_o, K = 0. ## Graph between Intensity of incident radiation and kinetic energy of photo electrons - Intensity of incident radiation and kinetic photo electric current are proportional. ## Stopping Potential - The value of negative potential provided to anode that can even stop electron having highest kinetic energy moving towards anode. - Stopping potential increases on increasing frequency of incident radiation. - Stopping potential is independent of intensity. ## Effect of frequency on stopping potential (same intensity) - Stopping potential is directly proportional to frequency. ## Effect of intensity on stopping potential - Stopping potential is independent of intensity. ## Limitations of Wave theory - Wave theory does not mention the concept of threshold frequency. - According to wave theory, energy of radiation depends on intensity but it depends on frequency. - According to wave theory, there should be a time lag between incident radiation and emission of electron but there is no such time lag. ## Photon - In interaction of radiation with matter, radiation behaves as if it is made up of particles called photons. Photons are a bundle or packet of energy. - E = hν, where h = 6.63 x 10^-34 J.s ## Properties of photons - The energy of photon is E = hν. - Photons are chargeless, have they do not get deflected by electric field and magnetic field. - Rest mass of photon is zero (photon rest में existनही करता) - massless. - Speed of photon in vacuum in 3 x 10⁸ m/s. - During collision, total energy and momentum remains constant but number of photons may change. ## Einstein and photoelectric equation - According to Planck's quantum theory light in made up of packet of energy or quanta called photon. - E = hν. - Einstein assumed that energy of photon (hν) can be used in two parts, one part of energy provides work function and other part provides. kinetic energy to photoelectrons. ## Work function W = hν_o - If ν = ν_o, hν_o = W + 0. - hν_o = W. ## Relation between potential (stopping potential), incident frequency and threshold frequency - KE = hν - W = eν_o. - eν_o = hν - W. - ν_o = (h/e) + (W/e). - ν_o = mν + c - Slope = m = h/e. - Intercept = c = -W/e or -Φ_o/e. ## Problem 1 In the study of a photoelectric effect, the graph between the stopping potential V_o and frequency ν of the incident radiation on two different metals P and Q is shown below. - Which one of the two metals has higher threshold frequency? - Determine the work function of the metal which has greater value? - Find the maximum energy of electron emitted by light of frequency 8 x 10¹⁴ Hz for this metal? ## Problem 2 - If there are two metals with their work function potassium (2.3 eV) and aluminium (4.3 eV). Identify which line represent which metal. - Write photoelectric equation that represent each of above graph and find slope of graph. - KE_max = hν - W ## Problem 3 If the frequency of incident radiation made double, what will be the new kinetic energy of photoelectrons? - K = 2K + W ## De Broglie Hypothesis & Derivation of wavelength - According to De Broglie Hypothesis, a wave is also associated with every particle which is called matter wave or De Broglie wave. - The wavelength of de Broglie wave is given by: λ = h/mv, where m is the mass of the body. - It is only associated with moving bodies. - It in not electromagnetic in nature. - For larger masses, wavelength of matter wave in smaller. Very-very smaller hence it cannot be noticed in daily life. ## Problem Let an electron is revolving in orbit with ν = 137c find wavelength associated with electron if c is the speed of light. - λ = 33.27 m ## Show graphically the variation of de Broglie wavelength (λ) - Potential (V) through which an electron is accelerated. - λ is inversely proportional to √V. - λ is directly proportional to 1/√V.