1. Nuclear Physics Micro-world Macro-world Lecture 16

2. Neutron By 1930, the charge and masses of many different nuclei were known. The charges were found to be Q nucleus = Z x proton charge & the masses were M nucleus = A x proton mass Z is always an integer A is nearly an integer But, except for hydrogen where A=Z=1, A & Z are different.

3. Electrons in the nucleus? One idea was that the nucleus contained A protons and A-Z electrons. But Heisenberg’s uncertainty principle forbids this: Suppose  x= 1x10 -14 m typical size of a nucleus  p x > 6.6x10 -34 Js 1x10 -14 m = 6.6x10 -28 kgm/s  v x > pxmepxme 6.6x10 -28 Js 9x10 -31 kg = >speed of light non-relativistic calculation is invalid Correct calculation gives E electron > 2x10 6 eV, such electrons would not stay inside a nucleus

4. Discovery of the neutron James Chadwick  Po Be n detector source No electric charge; mass ≈ proton mass

5. Nucleons (protons & neutrons) proton neutron mass 1.672x10 -27 kg 1.675x10 -27 kg mc 2 938.27 MeV 939.57 MeV Charge +1.6x10 -19 C 0 +

6. Isotopes Same chemistry; very different nuclear physics

7. Light isotopes AXAX Chemical symbol A = number of protons + neutrons Z Z=# of protons

8. All elements have isotopes 238 92 U 235 92 U

9. Nuclear force + + The very powerful electrical repulsion (100’s of Newtons) must be counteracted by some other very strong attractive force This new force is called the Strong Nuclear force

10. Strong Nuclear force Force Distance (x10 -15 m) 1.0 2.0 3.0 4.0 5.0 Attractive nuclear force repulsive electrical force attraction is stronger here repulsion is stronger here

11. Strong Nuclear Force It is very strong –It overcomes the electrical repulsion between positively charged protons that are only 10 -15 m apart. It acts over a very short range –It is not felt by nucleons when they are more than 10 -15 m apart. It is selective –It is felt by neutrons & protons, but not by electrons

12. Nuclei can’t be too large + + + + + + + + + + + + + + + A proton feels electrical repulsion from every proton in the nucleus It feels a Strong Nuclear attraction only to nearby nucleons In larger nuclei, the electrical force is bigger while the nuclear force stays the same. There are no stable nuclei above Z=82 (Lead) + + + + + + + + + Eventually, the electrical repulsion overwhelms the nuclear attraction

13. Discovery of radioactivity

14. Different types of radiation Marie Curie --- +++ neutral - charged  + charged  

15.  decay Z Y  Z-2 X + 2  A A-4 4

16. Conservation of energy in  decay Z Y  Z-2 X + 2  A A-4 4 parent daughters Energy of parent= Energy of daughters

17. Conserv. of energy in  decay Z Y  Z-2 X + 2  A A-4 4 parent daughters v = M X c 2 + M  c 2 + KE MYc2MYc2 KE = M Y c 2 - M X c 2 - M  c 2

18. Energy balance parent daughters the mass difference, times c 2, becomes KE

19. KE = M parent c 2 – (M daughters c 2 )  -particle Kinetic Energy Some mass is changed into Kinetic Energy All the a particles have the same Kinetic Energy

20. Z Y  Z+1 X + e - A n  p + e - Beta (  ) decay  + e - 6C6C 14 7N7N + + + + + + + + + + + + + 7p 7n 6p 8n

21. 88 Ra  89 Ac + e - 228 Other beta decays

22. 1 H  2 He + e - 3 Tritium Beta decay + e - 3H3H 3 He ++ +

23. Energy balance in beta decay 14 C 160 keV 14 N+e - 1 keV = 1000 eV

24. Electron energy in 14 C beta decay 160 keV KE e- None of the electrons have 160 keV of kinetic energy they all have less than that amount What has happened to the “missing” energy??

25. Pauli’s “desperate solution” no charge no mass Another “unseen” particle is emitted in  decay process

26. 6 C  7 N + e - + 14 14 C  decay revisited e-e- 6C6C 14 7N7N

27. 1 H  2 He + e - + 3 3 H  decay revisited e - 3H3H 3 He

28. Energy balance in beta decay parent KE e- + KE daughters

29. Cosmic gall NEUTRINOS, they are very small. They have no charge and have no mass And do not interact at all. The earth is just a silly ball To them, through which they simply pass, Like dustmaids down a drafty hall Or photons through a sheet of glass. They snub the most exquisite gas, Ignore the most substantial wall, Cold shoulder steel and sounding brass, Insult the stallion in his stall, And scorning barriers of class, Infiltrate you and me! Like tall and painless guillotines, they fall Down through our heads into the grass. At night, they enter at Nepal and pierce the lover and his lass From underneath the bed-you call It wonderful; I call it crass. John Updike

30. Radioactive half-life N = N 0 ( ½ ) n Number of remaining atoms Initial number of atoms number of halflives

31. Some half-lives 3 H (  3 He + e - + )12.3 yrs 14 C(  14 N + e - +  )5730 yrs 238 U(  234 Th +  )4.5x10 9 yrs 235 U(  231 Th +  )7.1x10 8 yrs 226 Ra(  222 Rn +  )1600 yrs 28 Mg(  28 Al + e - + )21 hrs 213 Po(  209 Pb +  )4x10 -6 s T 1/2

32. Carbon-14 dating

33. 14 C content

34. Shroud of Turin