1. End-of-semester info Final exam info:
Fri. May 6, 8-11am & Wed. May. 11, 8-11am
About 50 questions
Cumulative (all material from semester covered evenly)
Extra Practice problems (to be posted online today)
Focus on Lect material
Lectures next week:
Monday: Lect. 28 “Relativity”
Wednesday: in-class review of last lectures’ material
CHECK GRADEBOOK!
Online ICES evaluation!

2. Physics 102: Lecture 26
X-rays

3. X-Rays Photons with energy in approx range 100eV to 100,000eV.
This large energy means they go right through you (except for your bones).
What are the wavelengths?
.01 nm to 10 nm

4. X-Ray Production How do you produce 100 eV photons?
Black Body Radiation
Would require temperature over 10 times hotter than surface of sun
Excitation of outer electrons
Typically have energy around 10 eV
Radioactive Decays
Hard to turn on/off
E=13.6Z^2/n^2

5. Electron Tubes Example
Accelerate an electron through a voltage difference to give it some energy...
An electron is accelerated through a potential difference of 70,000 V. How much energy does it emerge with?
Recall from Lecture 3: EPE = V q
KE = EPE = (70,000 V) (1 e-)
= 1.6 x C
= 70,000 eV
= 11.2 x J
EPE of voltage gap becomes K.E. for electron.

6. From Electrons to X-Rays
Now take these high energy electrons (up to 100,000 eV) and slam them into heavy atoms - any element.
2 kinds of X-Rays are produced:
“Bremsstrahlung”
“Characteristic”

7. Bremsstrahlung X-Rays
Electron hits atom and slows down, losing kinetic energy.
Energy emitted as photon
Electron hitting atom makes many photons (X-Rays), all with different energy.
Many different wavelengths. 
intensity
Students should sketch graph. 0
If all of electron’s energy is lost to a single photon, photon has maximum energy (minimum wavelength).
Minimum X-Ray wavelength = lo.

8. Bremsstrahlung Practice
Example
An electron is accelerated through 50,000 volts
What is the minimum wavelength photon it can produce when striking a target?
Minimum wavelength Maximum energy
Electron loses ALL of its energy in one collision and emits one photon. 
intensity 0

9. Characteristic X-Rays
Electron knocks one of the two K shell (ground state) electrons out of an atom.
L (n=2) or higher shell electron falls down to K shell (ground state) and x-ray photon is emitted
K shell (n=1)
L shell (n=2) e-
(high energy electron) e-
Characteristic x-ray nomenclature
n=1 “K shell” n=2 “L shell” n=3 “M shell”

10. Characteristic X-Rays
Electron knocks one of the two K shell (ground state) electrons out of an atom.
L (n=2) or higher shell electron falls down to K shell (ground state) and x-ray photon is emitted e-
L shell (n=2) e- e- e- e-
ejected electron
Characteristic x-ray nomenclature
n=1 “K shell” n=2 “L shell” n=3 “M shell”
K shell (n=1) e- e-

11. Characteristic X-Rays
Electron knocks one of the two K shell (ground state) electrons out of an atom.
L (n=2) or higher shell electron falls down to K shell (ground state) and x-ray photon is emitted e-
L shell electron falls down e-
L shell (n=2) e- e-
X-Ray photon emitted
Characteristic x-ray nomenclature
n=1 “K shell” n=2 “L shell” n=3 “M shell”
K shell (n=1) e- e-
“K X-ray” (n= n=1 transition)

12. Ka X-Rays
Example
Estimate the energy of Ka X-rays off of a silver (Ag) target (Z=47).
Careful! the formula
assumed a single electron bound to just a positive nucleus.
Better formula for
multi-electron atoms L K
n=2
n=1
photon 
intensity Ka
(vs.
Expt)
Not bad!

13. Kb X-Rays Ka X-rays come from n=2 n=1 transition.
What about n= n=1 transition?
Not as likely, but possible. Produces Kb X-Rays!
Kb X-Rays are higher energy (lower l) than Ka. (and lower intensity) Kb  Ka
intensity
Different elements have different Characteristic X-Rays

14. All Together Now...
Brehmsstrahlung X-Rays and Characteristic X-Rays both occur at the same time. Kb  Ka
intensity 0
intensity  0 Kb  Ka
intensity

15. Preflight 26.1 K Kb K Kb intensity  
These two plots correspond to X-Ray tubes that:
(1) Are operating at different voltages
(2) Contain different elements
(3) Both
(4) Neither
Ka and Kb are the same
lo is different

16. ACT: X-Rays I K Kb intensity  0
Ka and Kb are the same for each! 
intensity 0
Higher voltage means higher energy x-ray photon can be produced, or smaller maximum wavelength, l0.
Which graph corresponds to the tube being operated at the higher voltage?
1) Top 2) Bottom

17. ACT: X-Rays II K Kb intensity  0
Energy of characteristic X-ray is proportional to (Z-1)2.
Higher energy = higher Z 
intensity 0
lo is the same for each!
The top spectrum comes from a tube with a silver target (Ag, Z=47). What is the bottom target?
1) Pd, Z=46 2) Ag, Z=47 3) Cd, Z=48

18. From atoms to nuclei to nucleons to quarks:
The hierarchy of sizes

19. Nuclear Physics A Z Nucleus = Protons + Neutrons nucleons
Z = proton number (atomic number)
Gives chemical properties (and name)
N = neutron number
A = nucleon number (atomic mass number)
Gives you mass density of element
A=N+Z

20. Strong Nuclear Force = (9 x 109)(1.6 x 10-19)2/10-15 = 2.3 x 10-13 J
Rutherford experiment shows that all the positive charge is contained in a small nucleus
Size ~ few x m (few fm)
Let’s estimate EPE of two protons separated by 1 fm
EPE = kq2/r
= (9 x 109)(1.6 x 10-19)2/10-15
= 2.3 x J
= 1.44 x 106 eV = 1.44 MeV
Therefore, the force that binds protons and neutrons together to form a nucleus must be very strong in order to overcome Coulomb repulsion
But the force acts over very short distances—of order few fm
Two atoms don’t feel force
Rutherford experiment: positive charge contained in tiny nucleus
Size of nucleus = few fm
Size of H atom = 0.05 nm = 50 fm
What keeps protons together?

21. Strong Nuclear Force Hydrogen atom: Binding energy =13.6eV neutron
(of electron to nucleus)
Coulomb force
electron
proton
neutron
proton
Simplest Nucleus: Deuteron=neutron+proton
(Isotope of H)
Very strong force
Binding energy of deuteron = or 2.2Mev! That’s around 200,000 times bigger!

22. Smaller is Bigger! Example Comparing Nuclear and Atomic sizes
Hydrogen Atom: Bohr radius =
Note the TREMENDOUS difference
Nucleus with nucl number A: A
has radius
Example Z
Nucleus is 104 times smaller and binding energy is 105 times larger!

23. Nuclei have energy level (just like atoms)
energy needed to remove a neutron from 12C is 18.7 MeV
energy needed to remove a proton from 12C is 16.0 MeV
12C energy levels
Note the energy scale is MeV rather than eV

24. See you next time!