Photoelectric Effect Lecture Notes PDF

10/3/24 Quantum Mechanics Classical (Newtonian) physics/mechanics begins to deteriorate on small scales. Quantum mechanics/physics is appropriate in the microscopic world. Quantum physics needs complex math to explain the behaviors and properties of small particles because the world of t...

10/3/24 Quantum Mechanics Classical (Newtonian) physics/mechanics begins to deteriorate on small scales. Quantum mechanics/physics is appropriate in the microscopic world. Quantum physics needs complex math to explain the behaviors and properties of small particles because the world of these subatomic particles is a very bizarre one, filled with quantum probabilities. 1 The Particle-Like Properties of Electromagnetic Radiation We will study early experiments that provided evidence that light, which we have treated as a wave phenomenon, has properties that we normally associate with particles. 2 1  10/3/24 Photoelectric Effect More Readings Serway 3.4 More Readings Thornton 3.6 3 The Photoelectric Effect The Photoelectric Effect: When a metal surface is illuminated with light, electrons could be emitted from the surface. e light In 1887 Heinrich Hertz e discovered this phenomenon during his research. 4 2  10/3/24 — Light falls on a metal surface (the emitter) in an evacuated tube. Light — It can release electrons CATHODE Emitter Collector ANODE which travel to the collector. Electrons I A Evacuated quartz tube V The Photoelectric Effect. 5 The released electrons have different kinetic energies (K) according to their binding energies (ΔE) to the metal. The work function Φ is the minimum energy needed to remove an electron from a certain material. e.g. Φ(Na) = 2.28 eV and Φ(Al) = 4.08 eV K = Elight - Δ E K1 K2 Kmax= 3 eV Kmax = Elight– Φ K3 K= 2 eV K= 3 eV K= 1eV Kmax= 3 eV K= 3 eV 4 eV 4 eV 4 eV 4 eV 4 eV 4 eV Φ = ΔE|min ΔE=2 eV ΔE=1 eV ΔE=3 eV ΔE=1 eV Φ=1 eV work function Φ metal Φ 3  10/3/24 Kmax is: The maximum kinetic energy of electrons. The energy of the most energetic electrons. The energy of the electrons that had the minimum binding energy (the work function) to the metal. 1 K max = m v 2max 2 7 — The stopping potential Vs : The potential that is just enough to repel the most energetic electrons (that have Kmax ). The potential at which the ammeter current drops to zero. At this point: -V s Kmax = e Vs e is the magnitude of the electron charge Kmax is the maximum kinetic energy of electrons 8 4  10/3/24 The classical point of view: — The surface of the metal is illuminated by an EMW of intensity I. An electron absorbs energy from the wave until the binding energy of the electron to the metal is exceeded, at which point the electron is released. e e e Remember As I increases Kmax increases and electrons need shorter time to be emitted. The experimental results: (1) Kmax (determined from Vs ) is totally independent of the intensity I of the light source. This result disagrees with -V s the classical wave theory which predicts that Kmax should Vs remains the same i.e. Kmax remains the same depend on I. 10 5  10/3/24 (2)The photoelectric effect does not occur if the frequency of the light source, f , is f o3 below a certain value called the f f o2 f o1 critical frequency or the threshold frequency fc or fo. If f > fc even if I is very weak electron emission If f < fc even if I is very strong No electron emission This result disagrees with the classical wave theory. 11 (3)The first photoelectron are emitted within 10 -9 s after the light source is turned ON , whatever the value of I. This result disagrees with the classical wave theory. It predicts a measurable time delay. 12 6  10/3/24 Einstein's Hypothesis 1905 — Einstein proposed that the energy of a light wave is concentrated in localized particles called "light quanta" or photons. — The energy of a photon is: E=h f h is Planck’s constant = 6.623 x 10-34 J.s f is the frequency of EMW hc E= E λ However, p= c Then, h E2 = Eo2 + p2c2. p= λ 13 Intensity of light = N h f where N is the number of photons per second per unit area Increasing the intensity of light means increasing the number of photons. The energy of each photon (hf) depends on the frequency of the wave not on the intensity. 14 7  10/3/24 Einstein Explanation for Photoelectric Effect: — A photoelectron is released as a result of absorbing a single photon. — The entire energy of the photon (hf ) is delivered instantaneously to a single electron. — If hf > Φ, the photoelectron will E= hf be released. f > Φ / h — If hf Φ, the excess energy appears as the kinetic energy of the most energetic electron: h f = Kmax + Φ Kmax = h f – Φ No relation with intensity of light — A photon of energy = Φ corresponds to light of frequency equal to the cutoff frequency f c. h fc = Φ 16 8  10/3/24 Doubling I means twice as many photons strike the surface and twice as many photoelectrons are released. In both cases Kmax is the same Intensity of light= N h f That is Kmax depends only on the frequency of the light. 17 Explanation of the experimental results: (1)Kmax (determined from Vs ) is totally independent of the intensity I of the light source. Kmax = hf - Φ No relation with intensity of light. Doubling I means twice as many photons strike the surface -V s and twice as many photoelectrons are released. In both cases Kmax and hence Vs are the same 18 9  10/3/24 (2)The photoelectric effect does not occur if the frequency of the light source, f , is below a f o3 certain value called the f o2 f o1 f critical frequency or the threshold frequency fc or fo. It depends on the Photoelectric Effect material. Kmax = h f - Φ If h f