Atomic Structure the wave nature of light 1 2 3 2 Hz 4 Hz 6 Hz  = frequency (s-1) (Hz)  = wavelength (m) u =   diffraction velocity ms-1

Electromagnetic radiation magnetic field electrical field  = frequency (s-1) (Hz)  = wavelength (m) u =   = c = speed of light = 2.998 x 108 ms-1

Problems not answered by classical physics 1. Black body radiation 1000 K red All objects at T > 0K emit radiation 1500 K orange atomic and molecular motion 2000 K white http://www.mhhe.com/physsci/astronomy/applets/Blackbody/frame.html E = n h ν energy is quantized frequency Planck’s constant h = 6.626 x 10-34J s integer Max Planck 1900 equation explained data but only certain quantities of energy could be emitted

Problems not answered by classical physics 2. Photoelectric effect e- e- e- e- e- e- light lens slit prism uv v b y o r ir potassium kinetic energy of e- independent of intensity dependent on wavelength number of e- independent of  (above threshold) dependent on intensity

Problems not answered by classical physics 2. Photoelectric effect Einstein 1905 light as particles photons with energy = hν e- e- e- low energy photons no electrons emitted above threshold energy all photons effective more photons more e- emitted higher energy photons higher K.E. to e-

Problems not answered by classical physics 3. Line spectra of atoms excited elements emit radiation specific frequencies Na Bohr 1913 Hg H He

Bohr atom n = quantum number n = 1 ground energy state stable n > 1 excited states unstable n = ∞ electron leaves atom ΔE = hν 1 nf2 1 ni2 ΔE = - RH Z2 - nuclear charge H = 1 2.178 x 10-18J

Bohr atom 1 nf2 1 ni2 ΔE = -2.178 x 10-18J - from n = 4 to n = 2 1 22 1 42 ΔE = -2.178 x 10-18J - ΔE = -4.084 x 10-19 J ΔE = hν 4.084 x 10-19 J = 6.626 x 10-34Js ν c =  ν = 6.17 x 1014s-1  = 486 nm green H line

Bohr atom Problems 1. Only works for H, He+, Li2+ 1 electron systems 2. Doesn’t explain why e- revolves at a fixed distance from nucleus De Broglie 1924 If light waves behave like particles, particles behave like light waves

De Broglie If light waves behave like particles, particles behave like light waves  = h/  = momentum = mv  = h/mv

De Broglie  = h/  = h/m Calculate the wavelength of an e- moving 62 ms-1  = 6.626 x 10-34 Js / 9.110 x 10-31kg x 62 ms-1  = 1.2 x 10-5 m = 1.2 x 104 nm = infrared De Broglie accelerate e- wavelength of x-rays

diffraction x-ray diffraction x-rays  = 7.1 nm same scale as atoms  = h/mv accelerate e-  = x-ray accelerated e- to 1.5 x 105 ms-1 electron diffraction  = 6.626 x 10-34 J s (9.110 x 10-31kg) (1.5 x 105 ms-1)  = 5.0 nm J = kg x m x s-2