{"id":10236,"date":"2026-07-03T17:39:42","date_gmt":"2026-07-03T17:39:42","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=10236"},"modified":"2026-07-03T17:39:42","modified_gmt":"2026-07-03T17:39:42","slug":"properties-of-waves-and-particles-and-photoelectric-effect","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/properties-of-waves-and-particles-and-photoelectric-effect\/","title":{"rendered":"Properties Of Waves And Particles And Photoelectric Effect"},"content":{"rendered":"
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KAPDEC® | Elite STEM Learning Platform | https:\/\/kapdec.com<\/a><\/p>\n

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Unit: <\/strong>Quantum, Atomic, and Nuclear Physics<\/strong><\/h2>\n

Chapter: <\/strong>Properties of Waves and particles and Photoelectric effect<\/strong><\/h3>\n

Reference: AP Physics Algebra, Quantum, Atomic, and Nuclear Physics, Quantum, Atomic, and Nuclear Physics, Properties of Waves and particles and Photoelectric effect, <\/em>Matter Wave, <\/em>Rutherford\u2019s Atomic Model, Bohr\u2019s Model & Energy Level Diagram<\/em>, <\/em>Rutherford\u2019s nuclear model of Atom<\/em>, <\/em>Alpha-Particle Trajectory, Electron Orbits, Bohr Model of the Hydrogen Atom, De Broglie\u2019s Explanation of Bohr\u2019s Second Postulate of Quantisation, Limitations of Bohr\u2019s model, Bohr\u2019s model however has many limitations,<\/em><\/p>\n

Photoelectric Effect<\/em><\/p>\n

After studying this chapter, you should be able to,<\/strong><\/p>\n

    \n
  • state the Radioactivity and Decay Law<\/li>\n
  • explain the concepts of Mass-Energy Equivalence<\/li>\n
  • state the concept of Atomic Masses and the Composition of the Nucleus<\/li>\n<\/ul>\n

    Matter Wave<\/strong><\/p>\n

    \u2022 Particle Nature of matter:<\/strong><\/p>\n

    Radiation behaves as if it is made up of particles in the interaction of radiation with matter, called photons. Each photon has energy E = hv and momentum<\/p>\n

    p=<\/strong>hv<\/em><\/strong>c<\/em><\/strong><\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

    \u00a0<\/strong>and speed c is the speed of light.<\/p>\n

    \u2022 Wave Nature of Matter:<\/strong><\/p>\n

    De Broglie proposed that the moving particles are associated with the waves. If a particle is having a momentum p, then the associated wavelength<\/p>\n

    \u03bb<\/em><\/strong>\u00a0=<\/strong>h<\/em><\/strong>p<\/em><\/strong>\u00a0=<\/strong>h<\/em><\/strong>mv<\/em><\/strong>\u00a0<\/strong>where v is the speed of the moving particle and its mass. The wavelength \u03bb<\/em>\u00a0is known as the de Broglie wavelength <\/em><\/strong>and the above relation is the de Broglie relation<\/em><\/strong>.<\/p>\n

    The wavelength of an electron accelerated with the potential V is:<\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

    \u2022 Heisenberg\u2019s uncertainty principle: <\/strong>This principle states that “it is not possible to measure both the position and momentum of an electron<\/p>\n

    at the same time exactly. There is always some uncertainty in the position and in momentum.<\/p>\n

    \u2022 The wave nature of electrons was verified and confirmed by the electron diffraction experiments performed by Davisson and Germer, and G.P. Thomson. Many other experiments later also confirmed the wave nature of the electron.<\/p>\n

    Rutherford\u2019s Atomic Model, Bohr\u2019s Model & Energy Level Diagram<\/strong><\/p>\n

    \u2022 Atoms in simple terms are defined as the smallest unit of matter.<\/p>\n

    \u2022 Atoms are electrically neutral because they contain the same number of electrons and protons.<\/p>\n

    Plum-Pudding Model<\/strong><\/p>\n

    \u2022 In 1898, J. J. Thomson proposed the first model of an atom.<\/p>\n

    \u2022 He stated, there is a uniform distribution of the positive charge of the atom throughout the volume of the atom and like seeds in a watermelon,<\/p>\n

    the negatively charged electrons are embedded in it. This model was picturesquely called the plum pudding model of the atom.<\/p>\n

    Alpha-Particle Scattering<\/strong><\/p>\n

    \u2022 Rutherford used a \u201cGold foil experiment\u201d<\/p>\n

    \u2022 Rutherford only identified one of type of radiation given off by radioactive elements like polonium, and uranium and named them as alpha particles.<\/p>\n

    Rutherford\u2019s nuclear model of Atom<\/strong><\/p>\n

    \u2022 According to Rutherford\u2019s model, the entire positive charge and most of the mass of the atom is concentrated in a small volume called the nucleus<\/p>\n

    with electrons revolving around the nucleus just as planets revolve around the sun.<\/p>\n

    \u2022 Rutherford scattering is a powerful way to determine an upper limit to the size of the nucleus.<\/p>\n

    \u2022 The alpha particles are fast-moving and positively charged Helium nuclei with two protons and two neutrons. Rutherford observed the deflection of alpha particles after passing through a metal sheet and proposed his atomic model<\/p>\n

    \u2022 After passing through the metal sheet, the alpha particles strike on the fluorescent screen which was coated with zinc sulphide and produced a visible flash of light<\/p>\n

    \u2022 He concluded that an atom consists of a minute positively charged body at its center called as nucleus. The nucleus, though small, contains all the protons and neutrons.<\/p>\n

    Alpha-Particle Trajectory<\/strong><\/p>\n

    \u2022 The trajectory traced by a particle depends on the impact parameter, b of collision.<\/p>\n

    \u2022 The particle near to the nucleus suffers large scattering.<\/p>\n

    \u2022 Only a small fraction of the number of incident particles rebound back indicating that the number of a-particles undergoing head-on collision is<\/p>\n

    small.<\/p>\n

    \u00a0<\/p>\n

    \u00a0<\/p>\n

    \"\"<\/p>\n

    Source: Kapdec.com<\/p>\n<\/div>\n

    Fig.: <\/strong>Alpha-Particle Trajectory<\/p>\n

    \u2022 Drawbacks of Rutherford\u2019s model: <\/strong><\/p>\n

    There were two major drawbacks in Rutherford’s nuclear model in explaining the structure of the atom:<\/p>\n

      \n
    • It cannot explain the characteristic line spectra of atoms of different elements.<\/li>\n
    • It contradicts the stability of matter because it speculates that atoms are unstable because the accelerated electrons revolving around the nucleus must spiral into the nucleus.<\/li>\n<\/ul>\n

      Electron Orbits<\/strong><\/p>\n

      \u2022 The electrostatic force of attraction, Fe between the revolving electrons and the nucleus provides the requisite centripetal force (Fc) to keep them in their orbits. Hence, for a dynamic states orbit in a hydrogen atom Fe = Fc<\/p>\n

      \u2022 The total energy of the electron is negative. It is given by<\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      Atomic Spectra<\/strong><\/p>\n

      \u2022 Each element has a characteristic spectrum of radiation, which it emits.<\/p>\n

      \u2022 Study of emission line spectra of material can therefore serve as a type of \u201cfingerprint\u201d for identification of the gas.<\/p>\n

      \u2022 The atomic hydrogen emits a line spectrum consisting of various series as:<\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      \u00a0<\/p>\n

      Bohr Model of the Hydrogen Atom<\/strong><\/p>\n

      Bohr combined classical and early quantum concepts, explained the spectrum of hydrogen atoms based on quantum ideas and gave his theory in the form of three postulates. These are:<\/p>\n

      \u00a0<\/p>\n

      \u2022 Bohr\u2019s first postulate was that an electron in an atom could revolve in certain stable orbits without the emission of radiant energy, contrary to the predictions of electromagnetic theory. According to this postulate, each atom has certain definite stable states in which it can exist, and each possible state has definite total energy. These are called the stationary states of the atom.<\/p>\n

      \u00a0<\/p>\n

      \u2022 Bohr\u2019s second postulate defines these stable orbits. This postulate states that the electron revolves around the nucleus only in those orbits for which the angular momentum is some integral multiple of h\/2\u03c0<\/em><\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      \u00a0where h is Planck’s constant (= 6.6 \u00d7 10\u2013 34<\/sup>Js). Thus, the angular momentum (L) of the orbiting electron is quantised. That is L = nh\/2 <\/em>\u03c0<\/em><\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      .<\/p>\n

      \u00a0<\/p>\n

      \u2022 Bohr\u2019s third postulate incorporated into atomic theory the early quantum concepts that had been developed by Planck and Einstein. It states that an electron might make a transition from one of its specified non-radiating orbits to another of lower energy. When it does so, a photon is emitted having energy equal to the energy difference between<\/p>\n

      the initial and final states. The frequency of the emitted photon is then given by<\/p>\n

      hv = Ei <\/sub>\u2013 Ef<\/sub>, where Ei<\/sub> and Ef<\/sub> are the energies of the initial and final states and Ei<\/sub> > Ef<\/sub>.<\/p>\n

      \u2022 Bohr radius is represented by the symbol a0<\/sub>, is given by<\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      \u2022 The total energy of the electron in the stationary states of the hydrogen atom is given by<\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      De Broglie\u2019s Explanation of Bohr\u2019s Second Postulate of Quantisation<\/strong><\/p>\n

      \u2022 De Broglie’s hypothesis provided an explanation for Bohr\u2019s second postulate for the quantisation of angular momentum of the orbiting electron. The quantised electron orbits and energy states are due to the wave nature of the electron and only resonant standing waves can persist.<\/p>\n

      \u2022 De Broglie\u2019s hypothesis is that electrons have a wavelength \u03bb<\/em>\u00a0=h\/<\/em>mv<\/em><\/p>\n

      Limitations of Bohr\u2019s model: Bohr\u2019s model however has many limitations.<\/strong><\/p>\n

      \u2022 It is applicable only to hydrogenic (single electron) atoms.<\/p>\n

      \u2022 It cannot be extended to even two electron atoms<\/p>\n

      such as helium.<\/p>\n

      \u2022 While Bohr’s model correctly predicts the frequencies of the light emitted by hydrogenic atoms, the model is unable to explain the relative intensities of the frequencies in the spectrum.<\/p>\n

      Photoelectric Effect<\/strong><\/p>\n

      \u2022 Work Function: <\/strong>The minimum energy which is necessary for an electron to get away from the surface of the metal is called the work function of the metal which is denoted by \u2205<\/em>0<\/em><\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      . The unit for measuring work function is electron volt (eV). This minimum energy can be provided by thermionic emission, field emission or photo-electric emission.<\/p>\n

      Thermionic emission: <\/strong>When a metal is heated, thermal energy is imparted to free the electrons from the surface of the metal.<\/p>\n

      Field emission: <\/strong>Electrons can be pulled out of metal by applying a very strong electric field (of the order of 108 <\/sup>Vm\u20131<\/sup>) to it, as in a Tesla coil.<\/p>\n

      Photo-electric emission: <\/strong>Electrons are emitted when a light of suitable frequency hits a metal surface. This can be seen in a photodiode.<\/p>\n

      \u2022 1eV is the energy attained by an electron when it has been accelerated by a potential difference of 1, so that 1eV = 1.602 \u00d7 10\u201319<\/sup>J.<\/p>\n

      \u2022 Photoelectric Effect: <\/strong>When metals are irradiated by light of suitable frequency, electrons start emitting from the metal surface. This phenomenon is known as the photoelectric effect.<\/p>\n

      \u00a0<\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      Fig.: <\/strong>Depiction of Photoelectric effect<\/strong><\/p>\n

      \u00a0<\/p>\n

      \u2022 Some metals are sensitive to ultraviolet light and some to visible light also. Photocurrent depends upon the intensity of light, frequency of incident light, and potential difference between both the plates and the material of the plate.<\/p>\n

      \u00a0<\/p>\n

      \u2022 Stopping Potential: <\/em><\/strong>Stopping potential or cut-off potential is the minimum retarding (negative) potential for which the photoelectric current stops at a particular frequency of incident light. It is denoted by V0<\/sub>.<\/p>\n

      \u00a0<\/p>\n

      \u2022 Saturation Current: <\/em><\/strong>At a certain potential difference, the photoelectric current stops increasing further. This maximum value of photocurrent is<\/p>\n

      known as the saturation current.<\/p>\n

      \u00a0<\/p>\n

      \u2022 Maximum Kinetic Energy: <\/em><\/strong>The maximum kinetic energy of the photoelectric electrons is denoted by Kmax <\/sub>and it depends directly on the frequency of the incident light. It is independent of the intensity of the light. The maximum kinetic energy Kmax <\/sub>= eV0<\/sub><\/p>\n

      \u00a0<\/p>\n

      \u2022 Threshold Frequency: <\/strong>The minimum cut-off frequency which is required for the emission of electrons is called the threshold frequency which is denoted by \u03bd0<\/sub>. No emission is possible for the frequency lower than the cut-off frequency.<\/p>\n

      \u00a0<\/p>\n

      \u2022 In the photoelectric effect, the light energy is converted into electrical energy. Photoelectric emission is a quick process having very less time lag.<\/p>\n

      \u00a0<\/p>\n

      \u2022 Effect of intensity of light on photocurrent:<\/strong><\/p>\n

      The number of photoelectrons emitted per second varies directly with the intensity of incident radiation.<\/p>\n

      \u2022 Effect of potential on the photoelectric current: <\/strong>The stopping potential is independent of its intensity for a given frequency of the incident radiation.<\/p>\n

      \u2022 Effect of frequency of incident radiation on<\/strong><\/p>\n

      stopping potential:<\/strong><\/p>\n

      The stopping potential V0 <\/sub>varies linearly with the frequency of incident radiation for a given photosensitive material.<\/p>\n

      There exists a certain minimum cut-off frequency v0 <\/sub>for which the stopping potential is zero.<\/p>\n

      \u00a0<\/p>\n

      \u2022 Einstein\u2019s Photoelectric Equation: <\/strong>Einstein proposed that light is comprised of small discrete energy packets known as photons or quanta and energy carried by each photon is hv, where v is the frequency of light and Planck\u2019s constant. The momentum carried by each photon is h<\/em>\u03bb<\/em><\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      \u00a0<\/p>\n

      \u00a0In the photoelectric effect, the emission is possible because of the absorption of a photon by an electron. The maximum kinetic energy of the emitted electron is:<\/p>\n

      \u00a0<\/p>\n

      K max = h\u03bd \u2212\u03c60<\/sub>, where \u03c60<\/sub> is the work function.<\/p>\n

      = h (\u03bd \u2212\u03bd0)<\/sub><\/p>\n

      The photoelectric emission is possible only when h\u03bd >\u03c60<\/sub> as Kmax <\/sub>must be non-negative.<\/p>\n

      \u21d2\u03bd >\u03bd0<\/sub> where<\/p>\n

      \u2022 From the photoelectric equation,<\/p>\n

      eV0<\/sub> = h\u03bd \u2212\u03c60<\/sub>, for \u03bd \u2265\u03bd0<\/sub> (as K max = eV0<\/sub>)<\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      \u00a0<\/p>\n

      or According to this result, the graph of V0 versus v is a straight line having a slope equal to h<\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      v.<\/p>\n

      Example:<\/strong> <\/strong>Assuming the mass of earth as 6.64 \u00d7 10<\/em>24<\/sup> kg and the average mass of the atoms that make up the earth as 40 u (atomic mass unit), the number of atoms in the earth is approximate _________<\/p>\n

      Solution: <\/strong><\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      \u00a0<\/p>\n

      Key Points:<\/strong><\/p>\n

      Wave nature:<\/strong> Waves exhibit characteristics such as interference, diffraction, and polarization.<\/p>\n

      Waveform:<\/strong> Waves have a characteristic shape, such as sine, square, or sawtooth.<\/p>\n

      Amplitude:<\/strong> The amplitude of a wave represents its maximum displacement or intensity.<\/p>\n

      Frequency:<\/strong> Frequency refers to the number of complete oscillations or cycles per unit of time, measured in hertz (Hz).<\/p>\n

      Wavelength:<\/strong> Wavelength is the distance between two consecutive points with the same phase on a wave. It is denoted by the symbol \u03bb (lambda) and is usually measured in meters (m).<\/p>\n

      Speed:<\/strong> The speed of a wave is the distance it travels per unit of time and is determined by the product of its frequency and wavelength.<\/p>\n

      Energy:<\/strong> Waves carry energy and the energy of a wave is related to its frequency. Higher frequencies correspond to higher energy waves.<\/p>\n

      Properties of Particles:<\/p>\n

      Particle nature:<\/strong> Particles are localized entities with definite positions at any given time.<\/p>\n

      Mass:<\/strong> Particles have mass, which determines their inertia and the force required to accelerate them.<\/p>\n

      Charge:<\/strong> Particles may carry an electric charge, either positive or negative, or be neutral.<\/p>\n

      Spin:<\/strong> Particles possess an intrinsic angular momentum called spin, which is quantized.<\/p>\n

      Quantum states:<\/strong> Particles can exist in discrete energy states, as described by quantum mechanics.<\/p>\n

      Wave-particle duality:<\/strong> Particles can exhibit both wave-like and particle-like behaviour, depending on the experimental setup and observation.<\/p>\n

      Photoelectric Effect Key Points:<\/strong><\/p>\n

      The photoelectric effect is the phenomenon where electrons are emitted from a material when it is exposed to light or electromagnetic radiation of sufficient frequency.<\/p>\n

      It was first explained by Albert Einstein in 1905, who proposed that light is composed of particles called photons, which carry discrete packets of energy.<\/p>\n

      \u00a0<\/p>\n

      \u00a0<\/p>\n

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      Key points<\/strong><\/p>\n

      \u00a0<\/p>\n

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      <\/p>\n