PHY 102: Waves & Quanta Topic 11 EM Radiation from atoms John Cockburn (j.cockburn@... Room E15)

1. PHY 102: Waves & Quanta Topic 11 EM Radiation from atoms John Cockburn (j.cockburn@... Room E15)

2. Broadband Thermal Radiation • “Blackbody” spectrum • Resolution of “ultraviolet catastrophe” • Atomic line spectra • Structure of the atom: Rutherford scattering

3. Thermal Radiation • Heat is associated with vibrational thermal motion of atoms/molecules • General principle: accelerating charged particles generate electromagnetic radiation (examples: generation of radio waves by moving electrons in antenna, generation of continuous X-ray spectrum by electrons decelerated by interaction with atoms of metal target) • So, e.m. radiation is generated by the thermally induced motion of atoms/molecules: THERMAL RADIATION….

4. Thermal Radiation • Unlike convection and conduction, transfer of heat by thermal radiation doesn’t require a “medium” • So, for example, heat can reach Earth from the Sun through millions of kilometres of empty space. • Rate at which an object, surface area A, temperature T, radiates energy is given by Stefan’s Law • = “Stefan’s constant” = 5.67 x 10-8 Wm-2K-4 e = “emissivity” ; 0< e < 1, depending on nature of surface For a “black body” (perfect emitter/absorber), e=1

5. Spectrum of emitted radiation Black body emission spectrum for various temperatures • Peak wavelength decreases with increasing temperature • Area under curve (total emitted power increases with increasing temperature • Experimentally, the dependence of peak wavelength on temperature is found to be given by:  (m) “Wien’s displacement law”

6. Modelling the black body spectrum • Rayleigh attempted to calculate the black body spectra from solids by assuming the material to consist of an assembly of classical oscillators, with each “normal mode” of vibration having energy kBT • Result: • Agrees OK at long wavelengths, but I at short wavelengths: “ultraviolet catastrophe” • Max Planck sorted this out in 1900 with the introduction of……. QUANTUM THEORY

7. Modelling the black body spectrum • Classical (Rayleigh) picture: • Oscillators have continuous spread of energies • Average energy of oscillator at temperature T = kT • Quantum (Planck) picture: • Oscillator only allowed to have energy in integer multiples of some constant times the oscillator frequency: E = nhf • Average energy of oscillator at temperature T:

8. Modelling the black body spectrum Obtain expression for spectral intensity by taking product of average energy per oscillator and number of oscillator modes per unit volume……. Planck result: • This model predicts the form of the blackbody spectrum perfectly, no “UV catastrophe” • First experimental “anomaly” to be explained by the need for a quantum theory (1900) • “h” originally introduced by Planck purely as an empirical constant to fit data…………………………

9. I(W/m3) Wavelength/m

10. Line spectra • “Hot” solids and liquids display the continuous emission spectra described above • “excited” gases display something completely different: LINE SPECTRA

11. Line spectra • Line spectrum of a gas of atoms/molecules is reproducible, and is a unique “fingerprint” of the gas • Suggests that the spectrum is somehow related to the internal structure of the atom………. • So, what is an atom???

12. The atom: a brief (incomplete) history Leucippus of Miletus, Democritus (~450BC) Suggest universe composed of hard, uniform, indivisible particles and the space between them (“atom” ≈ “cannot be cut”) Pierre Gassendi (1592-1655), Robert Boyle (1627-1691) Matter composed of rigid, indestructible atoms, varied size and form, different elements composed of different atoms, atoms can combine to form molecules………. Joseph Louis Proust (1754-1826), John Dalton (1766-1844) “Law of definite proportions”, atomic picture of chemical processes, stoichiometry Lothar Meyer (1830-95), Dmitry Mendeleev (1834-1907) Significance of atomic weights, Periodic Table of the elements

13. The atom: a brief (incomplete) history So, by the 19th century, it was universally accepted that matter was composed of atoms. But we still haven’t answered the question. What is an atom? 1897: JJ Thomson discovers electron, measures ratio e/m 1907: Millikan measures charge on electron ~1910: Thomson’s “plum pudding” model of the atom 1910-1911: Rutherford, Geiger and Marsden clarify internal structure of atom by scattering of positively charged -particles…………..

14. Rutherford Scattering Most -particles pass straight through, or deflected only slightly Some -particles deflected back through large angles

15. Rutherford Scattering • To explain results of the Rutherford scattering : • Atom must be mostly empty space • Positive charge must be concentrated in a small volume occupying a very small fraction of the total volume of the atom………… Nuclear model does work Christmas pudding model doesn’t work Atomic radius ~ 10-10m Nuclear radius ~ 10-14m