Brian Wecht, the TA is back!
Pl. give all regrade requests to him
Quiz 4 is This Friday : Chapter 3
Emphasis will be On the Rutherford Scattering & The Bohr Atom
Rutherford Scattering & Size of Nucleus
distance of closest appoach∝ r size of nucleus 1 Kinetic energy of α = K = mv2 ααβ2 α particle will penetrate thru a radius r nucleus until all its kinetic energy is used up to do work AGAINST the Coulomb potential of the Nucleus: 1 ()()Ze2 e K = mv2 = 8 MeV= k αβ2 α r 2kZe2 ⇒ r = Kα
For Kα =7.7.MeV, Z Al = 13 2kZe2 ⇒= rm= 4.9×10−15 Kα nucleus Size of Nucleus = 10-15m Size of Atom = 10-10m Spectral Observations : series of lines with a pattern
• Empirical observation (by trial & error) • All these series can be summarized in a simple formula 111⎛⎞ =−Rnnn⎜ ⎟,,1,2,3,4.. >= ⎜ 22⎟ fii λ ⎝⎠n fin Fitting to spectral line series data Rydberg Constant R=1.09737 × 1071m− How does one explain this ?
Bohr’s Bold Model of Atom: Semi Quantum/Classical -e m 1. Electron in circular orbit e around proton with vel=v 2. Only stationary orbits F allowed . Electron does not V radiate when in these stable +e (stationary) orbits r 3. Orbits quantized: –Mevr = n h/2π (n=1,2,3…) 4. Radiation emitted when electron “jumps” from a stable orbit of higher energy e2 Ur()=− k Æ stable orbit of lower r energy Ef-Ei = hf =hc/λ 5. Energy change quantized 1 2 KE= m v • f = frequency of radiation 2 e Reduced Mass of 2-body system -e me General Two body Motion under a central force F V +e
reduces to r
me • Both Nucleus & e- revolve around their common center of mass (CM) • Such a system is equivalent to single particle of “reduced mass” µ that revolves around position of Nucleus at a distance of (e- -N) separation