Goal: To understand the atom

1. Goal: To understand the atom Objectives: To learn that The basics of Atomic Physics isn’t so bad To understand the Bohr atom To understand Electron energy levels To understand how energy levels lead to Absorption and emission To learn about the Electron shell radius To apply 3-5 to Bigger atoms

2. Atomic Physics • Just like with relativity, the basics isn’t too bad. • It does get a lot more complicated when you add in the small details, but we won’t do that. • An atom consists of a nucleus + electron shells. • The nucleus has protons and neutrons and is about 10-14 m in size. • The electron shells might have electrons. • The shell closest to the nucleus is called the ground state.

3. Bohr Atom • The Bohr Atom is the most basic atom. • It is basically a Hydrogen atom. • It consists of 1 proton and 1 electron. • The electron orbits around the proton in a shell – often times the ground state shell. • Each other shell is further away. • Each is assigned a number. • The ground state is n=1, and they go to n = infinity.

4. Energy Levels • The electron has energy levels. • Just like with orbits the closer to the nucleus the lower the energy. • Energy goes to 0 as the electron leaves the atom. • So, to go travel from energy levels the electron has to gain or loose energy.

5. Absorption/Emission • To go up in energy levels an electron must absorb a photon. • The electron can ONLY absorb a photon if it is the exact energy needed to get to the higher energy level. • Conversely, when it goes back every time it goes down a lvl it emits a photon. • The atom can go all the way down at once but usually it goes down 1 step at a time. • What direction will the electron emit the photon?

6. Energy Equations • I bet you are expecting something crazy and complicated derived from potential energies, ect. • Yes, I could do that, but I won’t. • When you get through all of that here is what you come up with: • E = -13.6 eV / n2 • Example: an electron in a normal Hydrogen atom is in the n = 2 energy state. What is the energy of the electron?

7. Energy from transitions • If you go from an initial energy state (ni) to some final state (nf) then you will get a change in energy (that will correspond to either an absorption or emiision of a photon). • The change in energy is Ef – Ei • So, E = Ef – Ei = -13.6 eV (1/nf2 – 1/ni2) • If this value is negative you get an emission of a photon. • If negative you have an emission of a photon.

8. Example • An electron goes from the n=5 to the n=1 state. • What is he change in energy for the photon? • Will this result in an absorption of a photon or emission? • What will be the wavelength of the photon (hint: E = hc / λ and h = 4.136 * 10-15 eV*s)?

9. wavelength • There is one more expression for wavelength: • 1/ λ = R (1/nf2 – 1/ni2) • R Is called the Rydberg constant and is 1.097 * 107 1/m • I don’t find this equation very useful because you can get this all from the other equation, but you might have to use it on the homework.

10. Electron shell radius • How far away from the nucleus is the electron? • This one you can get from looking at angular momentum. • L = nħ = mvr • Once you play around with that you get: • a0 = ħ2 / (me k e2) • a0 is called the Bohr radius and is the radius for the ground state (n=1) • a0 = 0.0529 nm • For any other energy level: • r = a0 * n2

11. Sample • An electron is at the n = 10 energy state. • What is the electrons radius around the nucleus?

12. Bigger atoms • What about bigger atoms than Hydrogen that have more protons? • Most protons means more charge in the nucleus and that means more force and lower potential energies. • Also, the shell radii will change. • But by what amount?

13. 1 electron atoms • This all applies to atoms with only 1 electron. • After 1 electron all the electrons repulse each other so you get changes – in a very complicated way that we will not cover in this course. • r =a0 * n2 / Z • E depends on q/r, so will depend on Z2. • So, E = -13.6 eV * Z2 * (1/nf2 – 1/ni2) • Quick sample: If an electron in an oxygen atom (Z=8) drops from the n=5 to the n=4 state then what is the energy of the emitted photon?

14. Photon energy to Mass energy and back • Since matter and photons are 2 forms of energy it is possible to convert from one to the other. • One way is called “pair production”. • In this case a photon becomes an electron and a positron (an anti electron) • The positron can run into an electron later. • When it does, both the positron and electron will be converted to pure energy (as 2 photons). • Since the mass energy of an electron or positron is 511k eV that would be the energy of the photon (well maybe a bit more if the particles had some kinetic energy).

15. Conclusion • We have learned about atoms. • We learned about the Bohr atom. • We learned about energy levels for electrons and what it takes to go up and down in energy levels. • We learned about larger atoms with only 1 electron.