1. Atomic Structure

2. Model A: The plum pudding model J.J. Thompson Negative charges like raisins in plumb pudding Positive charge is spread out like the pudding

3. detector Fire a beam of alpha particles (He nucleii with charge +2) at a thin gold foil. Watch what happens.

4. detector What would Thompson’s model predict? Collisions? Sticking? Bouncing? What was observed: 1) most alpha particles passed through undeflected by the gold foil. 2) some were deflected at large angles 3) some were deflected backwards!

5. Rutherford’s Solution: The atom is composed of a concentrated region of positive charge at its center known as the nucleus. Negative charges (electrons) followed circular orbits around the nucleus. New problem: According to Maxwell, an accelerating electron will radiate energy. Since the electrons have centripetal acceleration, they should radiate.

6. In addition, the frequency of the emitted light will match the frequency of the orbit of the electron around the nucleus. What did you find in the lab when you looked at the Hydrogen spectrum? This implies a continuous spectrum of emitted radiation should be observed. Only a few colors (wavelengths).

7. The emission spectrum of your second source (Helium or Mercury) looked very different than the Hydrogen source! Each element has its own unique emission spectrum -- a spectral FINGERPRINT! Each element has its own unique emission spectrum -- a spectral FINGERPRINT! Experimentally, the observed lines in the visible part of the Hydrogen spectrum are found at wavelengths given by: n = 3, 4, 5,...

8. The constant R H is found to be: So we only observe emitted radiation at a discrete set of wavelengths. Furthermore, atoms absorb radiation at only a discrete set of wavelengths as well. Balmer Series n = 3, 4, 5,...

9. These two sets (the emission spectrum and the absorption spectrum) are identical. The latter is known as the absorption spectrum. Which is to say, if we shined light with uniform intensity across the entire spectrum through a gas cloud of a single type of atom, radiation would be missing from the resulting spectrum as this discrete set of wavelengths.

10. 410.2nm434.1nm486.1nm656.3nm Emission Spectrum Absorption Spectrum

11. So how do we explain the fact that only discrete wavelengths are absorbed/emitted from the atoms? Bohr’s Solution: 1) Only certain electron orbits are stable 2) Stable orbits have quantized angular momentum. 3) Radiation is emitted when electrons “jump” from one orbital to another. 4) The energy of the emitted radiation is proportional to the energy difference between the orbitals.

12. Recall from Physics 111 that the angular momentum of a point mass in a circular orbit of radius r is given by L = m v r Bohr’s suggested that only certain values of L resulted in stable orbits. The orbitals which had n = 1, 2, 3,... were stable.

13. To figure out the total energy of the electrons in these orbitals, recall Total Energy = KE + PE

14. We also know from Newton’s Second Law that the electrical force of attraction between the proton and the electron must balance the centripital force the electron feels in orbit. Which means that the kinetic energy is given by:

15. So the energy of the electron orbitals is given by: Recall, however, that not all orbitals are possible. Only the ones with quantized angular momentum are allowed:

16. Solving for v and squaring... Compare with the force balance... Solving for v 2... Setting these two equal to one another... Setting these two equal to one another...

17. Solving for r tells us the allowed orbitals. Where a 0 is called the “Bohr Radius” The smallest allowed orbital a 0 = 0.0529 nm

18. Plugging our quantized values of r into our equation for the energy of the electron orbitals gives us: An atom is said to be in the “ground state” when n = 1. Now we can predict the energy of the emitted radiation when an electron “jumps” from one orbital to another...

19. And we know the energy of a photon is Look familiar?

20. Empirical results for the Balmer series... derived results

21. A photon of the correct frequency interacts with the electron. The photons energy is absorbed by the atom. The electron jumps to a higher orbital.

22. The electron jumps to a lower orbital (lower energy state). A photon is emitted with exactly the amount of energy lost as the electron falls to the lower orbital.