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. 22-28 material Lectures next week: Monday: Lect. 28 “Relativity” Wednesday: in-class review of last lectures’ material CHECK GRADEBOOK! Online ICES evaluation!

Physics 102: Lecture 26 X-rays

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

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

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 10-19 C = 70,000 eV = 11.2 x 10-14 J EPE of voltage gap becomes K.E. for electron.

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”

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.

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

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”

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-

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=2 n=1 transition)

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!

Kb X-Rays Ka X-rays come from n=2 n=1 transition. What about n=3 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

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

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

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

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

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

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

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 10-15 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 10-13 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?

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!

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!

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

See you next time!