Dual Nature Of Matter & Radiation PDF

CHAPTER Dual Nature of 11 Radiation and Matter Planck’s Quantum Theory Stopping potential is indepen...

CHAPTER Dual Nature of 11 Radiation and Matter Planck’s Quantum Theory Stopping potential is independent of intensity of light used. ™According to Planck’s quantum theory, light is considered to ™ The number of photoelectrons emitted per second is directly be made up of small packets (or particles) of energy known proportional to the intensity of the incident radiation. as quanta of energy or radiation. ™ The maximum kinetic energy of the ejected electrons is hc 12400 independent of the intensity of incident radiation but depends Energy, E = hν = = eV λ λ (Å) upon the frequency of the incident radiation. Photons Radiation Pressure h I ™ Momentum of one photon is. Radiation pressure, = P (1 + r ). Here I is the intensity of λ c ™ When radiation interacts with matter, the radiation behaves as incident radiation, c is the speed of light and r is the reflectivity if it is made of particles like photons. of the surface. ™ Einstein proposed that electromagnetic radiation (or simply For 100% reflection, r = 1 and for 100% absorption r = 0. light) is quantized and exists in elementary amounts (quanta) that we now call photons. de-Broglie Hypothesis ™ Photons are not deflected by electric and magnetic fields ™ It says that a wave is associated with a moving material which shows that they are neutral and do not carry any charge. particle. The wavelength associated with a moving particle is ™ The energy of photon depends upon the frequency of radiation h but is independent of the intensity of radiation. given by λ = , where m is the mass of the particle moving mv Photoelectric Effect with v velocity and h is Planck’s constant. This wave is called ™ When light of suitable frequency illuminates a metal de-Broglie wave. surface, electrons are emitted. This process of ejection of Key Tips electrons using light is known as photoelectric emission. Photoelectrons ejected from metal have kinetic energies h ™ de-Broglie wavelength of a material particle, λ = ranging from 0 to Kmax. mv ™ A certain minimum amount of energy is required for an ™ de-Broglie wavelength in terms of energy of a particle (E), electron to be pulled out from the surface of a metal. This h minimum energy is called the work function (φ) of that metal. λ= 2mE Work function is minimum for cesium (1.9 eV). ™ Einstein equation for photoelectric effect is, ™ de-Broglie wavelength of an electron accelerated through a hc hc 150 12.27 hv = φ + KEmax ⇒ = + eVs potential V volt, = λ = Å Å λ λ0 V V ™ The minimum frequency of the incident light below which ™ de-Broglie wavelength of a particle in terms of temperature photoelectrons are not ejected from the metal surface is h known as threshold frequency (ν0). (T), λ = hc 3mkT Work function, =φ hv= 0 λ0 Heisenberg’s Uncertainty Principle λ0 = threshold wavelength According to Heisenberg’s Uncertainty Principle, it is not ™ The minimum negative potential given to the metal plate with possible to measure exactly both the position and momentum of a respect to the collector at which the photoelectric current microscopic particle (say electron) at the same time. That is, becomes zero is known as stopping potential or cut-off  h potential. Here KEmax = eVs , Vs = stopping potential ∆x∆p ≥ , where  = , 2 2π