{"id":9460,"date":"2026-06-01T21:33:48","date_gmt":"2026-06-01T21:33:48","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=9460"},"modified":"2026-06-01T21:33:48","modified_gmt":"2026-06-01T21:33:48","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":"

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’s Atomic Model, Bohr’s Model & Energy Level Diagram<\/em>, <\/em>Rutherford’s nuclear model of Atom<\/em>, <\/em>Alpha-Particle Trajectory, Electron Orbits, Bohr Model of the Hydrogen Atom, De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation, Limitations of Bohr’s model, Bohr’s 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

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

    • 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

    λ<\/em><\/strong> =<\/strong>h<\/em><\/strong>p<\/em><\/strong> =<\/strong>h<\/em><\/strong>mv<\/em><\/strong> <\/strong>where v is the speed of the moving particle and its mass. The wavelength λ<\/em> is 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

    • Heisenberg’s 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

    • 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’s Atomic Model, Bohr’s Model & Energy Level Diagram<\/strong><\/p>\n

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

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

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

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

    • 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

    • Rutherford used a “Gold foil experiment”<\/p>\n

    • 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’s nuclear model of Atom<\/strong><\/p>\n

    • According to Rutherford’s 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

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

    • 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

    • 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

    • 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

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

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

    • 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

     <\/p>\n

     <\/p>\n

    \"\"<\/p>\n

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

    • Drawbacks of Rutherford’s 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

      • 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

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

      \"\"<\/p>\n

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

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

      • Study of emission line spectra of material can therefore serve as a type of “fingerprint” for identification of the gas.<\/p>\n

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

      \"\"<\/p>\n

       <\/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

       <\/p>\n

      • Bohr’s 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

       <\/p>\n

      • Bohr’s 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\/2π<\/em>\"\" where h is Planck's constant (= 6.6 × 10– 34<\/sup>Js). Thus, the angular momentum (L) of the orbiting electron is quantised. That is L = nh\/2 <\/em>π<\/em>\"\".<\/p>\n

       <\/p>\n

      • Bohr’s 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>– Ef<\/sub>, where Ei<\/sub> and Ef<\/sub> are the energies of the initial and final states and Ei<\/sub> > Ef<\/sub>.<\/p>\n

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

      \"\"<\/p>\n

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

      \"\"<\/p>\n

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

      • De Broglie's hypothesis provided an explanation for Bohr’s 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

      • De Broglie’s hypothesis is that electrons have a wavelength λ<\/em> =h\/<\/em>mv<\/em><\/p>\n

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

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

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

      such as helium.<\/p>\n

      • 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

      • 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 ∅<\/em>0<\/em>\"\". 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–1<\/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

      • 1eV is the energy attained by an electron when it has been accelerated by a potential difference of 1, so that 1eV = 1.602 × 10–19<\/sup>J.<\/p>\n

      • 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

       <\/p>\n

      \"\"<\/p>\n

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

       <\/p>\n

      • 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

       <\/p>\n

      • 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

       <\/p>\n

      • 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

       <\/p>\n

      • 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

       <\/p>\n

      • 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 ν0<\/sub>. No emission is possible for the frequency lower than the cut-off frequency.<\/p>\n

       <\/p>\n

      • 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

       <\/p>\n

      • 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

      • 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

      • 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

       <\/p>\n

      • Einstein’s 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’s constant. The momentum carried by each photon is h<\/em>λ<\/em>\"\"<\/p>\n

       <\/p>\n

       In 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

       <\/p>\n

      K max = hν −φ0<\/sub>, where φ0<\/sub> is the work function.<\/p>\n

      = h (ν −ν0)<\/sub><\/p>\n

      The photoelectric emission is possible only when hν >φ0<\/sub> as Kmax <\/sub>must be non-negative.<\/p>\n

      ⇒ν >ν0<\/sub> where<\/p>\n

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

      eV0<\/sub> = hν −φ0<\/sub>, for ν ≥ν0<\/sub> (as K max = eV0<\/sub>)<\/p>\n

      \"\"<\/p>\n

       <\/p>\n

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

      Example:<\/strong> <\/strong>Assuming the mass of earth as 6.64 × 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

       <\/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 λ (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

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

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       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

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

       <\/p>\n

       <\/p>\n","protected":false},"excerpt":{"rendered":"

      Unit: Quantum, Atomic, and Nuclear Physics Chapter: Properties of Waves and particles and Photoelectric effect Reference: AP Physics Algebra, Quantum, Atomic, and Nuclear Physics, Quantum, Atomic, and Nuclear Physics, Properties of Waves and particles and Photoelectric effect, Matter Wave, Rutherford’s Atomic Model, Bohr’s Model & Energy Level Diagram, Rutherford’s nuclear model of Atom, Alpha-Particle Trajectory, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[623],"tags":[],"class_list":["post-9460","post","type-post","status-publish","format-standard","hentry","category-ap-physics-2"],"_links":{"self":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/9460","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/comments?post=9460"}],"version-history":[{"count":0,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/9460\/revisions"}],"wp:attachment":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/media?parent=9460"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/categories?post=9460"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/tags?post=9460"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}