Lecture 8. > Blackbody Radiation. > Photoelectric Effect

Transcription

1 Lecture 8 > Blackbody Radiation > Photoelectric Effect *Beiser, Mahajan & Choudhury, Concepts of Modern Physics 7/e French, Special Relativity *Nolan, Fundamentals of Modern Physics 1/e Serway, Moses & Moyer, Modern Physics 3/e Taylor & Wheeler, Spacetime Physics 2/e Tipler & Llewellyn, Modern Physics 5/e 1

2 Particles and Waves > Particles: definite place in space, localized > Waves: spread out, propagates through space > Independent treatment of particles and waves: describing electrons Maxwell ~ Accelerating charges generate perpendicular electric and magnetic fields ~ From Faraday: changing B yields E, induced current ~ Varying fields produce each other Proof by Hertz ~ Light is an EM wave ~ Red: 4.3 x 10^(14) Hz ~ Violet: 7.5 x 10^(14) Hz 2

3 Particles and Waves contd > Superposition principle: The amplitude of a wave at any point in time in a point in space is the sum of the amplitudes of individual waves at that time in that point in space. > Wave interference: constructive & destructive interference Thomas Young + Diffraction: patterns of light and dark bands of light + Wave property: particles don't behave this way 3

4 Blackbody Radiation > Radiation in general + Light followed Maxwell's theory + The way radiation is observed shows otherwise + All objects radiate at a given frequency, depending on the temperature > Blackbody: an ideal material that absorbs all radiation in contact w/ it + Good absorber = good emitter + Warmer objects emit at a higher frequency > Consider a wave in a box + Energy density: Lord Rayleigh, James Jean + Whole number of half wavelengths 4

5 Blackbody Radiation contd > Rayleigh-Jean equation for energy density: + Equipartition principle c 3 for every degree of freedom, (½) kt of energy is given + Boltzmann's constant: x 10^(-23) J/K + For harmonic oscillators, there are 2 degrees of freedom: kinetic + potential u(ν) d ν= ɛ G (ν) d ν= > Radiation rate ~ energy density > Blows up for large frequencies > Ultraviolet catastrophe 8π kt c 3 ν 2 d ν G(ν) d ν= 8π ν2 d ν ɛ=kt 5

6 Blackbody Radiation contd > 1900 Max Planck: gone for high frequencies, reduces to Rayleigh-Jean for low frequencies > Discrete oscillations only: n = 0, 1, 2, ɛ n =n h ν > Planck's constant: h = x 10^(-34) J-s > Average energy: u(ν) d ν= 8π h c 3 ν 3 d ν exp (h ν/ kt ) 1 ɛ= h ν exp (h ν/ kt ) 1 6

7 Photoelectric Effect > Light incident on a metal releases electrons, receiving energy + Photoelectrons + Metals > Set-up: cathode-anode in vacuo > Observations 1. Emission is instant 2. Intensity has no effect on photoelectron energy 3. A minimum frequency appears + Not explained by the wave picture of light 7

8 Photoelectric Effect contd > Einstein: treat light as a quantum (pl quanta) + Photons: energy determined by their frequency + Explains the three observations E=h ν > Work function: minimum energy needed to dislodge the electron ϕ=h ν 0 > Thus, h ν= K max +ϕ 8

9 Summary > Blackbody radiation quantizes energy > Photoelectric effect shows that light is quantized 9

10 Sample Problems 1. The threshold wavelength for photoelectronic emission for a particular material is 518 nm. Find the work function for this material. 2. A photon has an energy of 5.00 ev. What is its frequency and wavelength? 3. The maximum wavelength for photoelectric emission in tungsten is 230 nm. What wavelength of light must be used in order for electrons with a maximum energy of 1.5 ev to be ejected? 10