Dual Nature of Radiation and Matter Minimum energy required by an electron to escape from the metal surfaceis called the work function of the metal. Thermionic emission: By heating, sufficient thermal energy can be imparted to the free electrons to enable them to come out of the metal. Field emission : By applying a very strong electric field to a metal, electrons can be pulled out of the metal, as in a spark plug. Photo-electric emission : When light of suitable frequency illuminates a metal surface, electrons are emitted from the metal surface. These photo(light)-generated electrons are called photoelectrons. The maximum value of the photoelectric current is called saturation current. The minimum negative (retarding) potential V0${V}_{0}$ given to the plate A for which the photocurrent stops or becomes zero is called the cut-off or stopping potential. For a given frequency of the incident radiation, the stopping potential is independent of its intensity. The maximum kinetic energy of photoelectrons depends on the light source and the emitter plate material, but is independent of intensity of incident radiation. Effect of frequency of incident radiation on stopping potentiala. The graph shows that the stopping potential V0 varies linearly with the frequency of incident radiation for a given photosensitive material.b. there exists a certain minimum cut-off frequency Q0 for which the stopping potential is zero. The maximum kinetic energy of the photoelectrons varies linearly with the frequency of incident radiation, but is independent of its intensity. For a frequency 𝜈$𝜈$ of incident radiation, lower than the cut-off frequency 𝜈0 ${𝜈}_{0}\phantom{\rule{0.22em}{0ex}}$ , no photoelectric emission is possible even if the intensity is large.This minimum, cut-off frequency 𝜈0${𝜈}_{0}$, is called the threshold frequency. Wave Nature of Light: interference, diffraction and polarization Particle Nature of light: Photo electric effect, Compton effect De Broglie relation 𝜆=hp=hmv$𝜆=\frac{h}{p}=\frac{h}{mv}$ Photons are electrically neutral and are not deflected by electric and magnetic fields. Energy of photon, E=h 𝜈 $E=h\phantom{\rule{0.22em}{0ex}}𝜈\phantom{\rule{0.22em}{0ex}}$ Momemtum of photon, p=h 𝜈c $p=\frac{h\phantom{\rule{0.22em}{0ex}}𝜈}{c}\phantom{\rule{0.22em}{0ex}}$
 Questions Q.11.1.Find the(a) maximum frequency, and(b) minimum wavelength of X-rays produced by 30 kV electrons.A.11.1.(a)Charge of one electron=-1.6×10-19 C$=-1.6×{10}^{-19}\phantom{\rule{0.22em}{0ex}}C$Energy in electron=30kV=30000×1.6×10-19 J $=30kV=30000×1.6×{10}^{-19}\phantom{\rule{0.22em}{0ex}}J\phantom{\rule{0.22em}{0ex}}$E=h𝜈$E=h𝜈$⟹30000×1.6×10-19=6.63×10-34 𝜈 $⟹30000×1.6×{10}^{-19}=6.63×{10}^{-34}\phantom{\rule{0.22em}{0ex}}𝜈\phantom{\rule{0.22em}{0ex}}$⟹𝜈=7.23982×1018 Hz $⟹𝜈=7.23982×{10}^{18}\phantom{\rule{0.22em}{0ex}}Hz\phantom{\rule{0.22em}{0ex}}$ (b)c=𝜈𝜆$c=𝜈𝜆$⟹𝜆=c𝜈=3×1087.23982×1018=0.414375×10-10 m$⟹𝜆=\frac{c}{𝜈}=\frac{3×{10}^{8}}{7.23982×{10}^{18}}=0.414375×{10}^{-10}\phantom{\rule{0.22em}{0ex}}m$⟹𝜆=0.0414375×10-9 m=0.0414375 nm$⟹𝜆=0.0414375×{10}^{-9}\phantom{\rule{0.22em}{0ex}}m=0.0414375\phantom{\rule{0.22em}{0ex}}nm$