Announcements The ECAFE evaluation system is now open. Please take a few minutes to review the course. Today: Nuclear Spin example, radioactivity, radioactive decay law and half-life. Quiz 32 will be given by Professor Lam. Today will have some clicker questions. Not required but inspiring and interesting. (29min BBC documentary on the birth of quantum mechanics. The part about the Solvay conference is especially good) https://www.youtube.com/watch?v=LLvihoOeNpI

Intuition: Some interesting nuclear physics simulations PHET simulation of NMR (Hint: Larmor frequency 42.58 MHz/T) https://phet.colorado.edu/en/simulation/legacy/mri PHET simulation of alpha radioactive decay: https://phet.colorado.edu/en/simulation/legacy/alpha-decay PHET simulation of a beta decay https://phet.colorado.edu/en/simulation/legacy/beta-decay PHET simulation of nuclear fission https://phet.colorado.edu/en/simulation/legacy/nuclear-fission

Nuclear spin example Protons are placed in a 2.30 T field that points in the z-direction. What is the energy difference between the states with the spin parallel or anti-parallel to the B field ? A proton can make a transition between these states, what is the wavelength of the photon emitted ?

Nuclear spin example Protons are placed in a 2.30 T field that points in the z-direction. What is the energy difference between the states with the spin parallel or anti-parallel to the B field ? Remember the proton has a magnetic moment that is 2.7928 μn This is just the energy when aligned. The energy when anti-parallel is U=+2.025 x 107eV. Do you see why ?

Nuclear spin example Protons are placed in a 2.30 T field that points in the z-direction. A proton can make a transition between these states, what is the wavelength of the photon emitted ? Question: Is the transition photon an x-ray, a gamma ray, in the visible, infrared, or radio range ?

Nuclear spin example Protons are placed in a 2.30 T field that points in the z-direction. A proton can make a transition between these states, what is the wavelength of the photon emitted ? Question: Is this the same as the 21 cm hyperfine transition that we discussed earlier ? (Yes or no, explain) Ans: No, the 21 cm line arises from the interaction of electron spin magnetic moment and nuclear spin moment but also corresponds to a spin flip. It does not involve an external B field.

Experimentalist’s viewpoint (α, β, γ) Penetration (explain) How they bend in a magnetic field (explain)

A beta-minus β– particle is an electron. (example Co60) Beta and gamma decay There are three types of β decay: β- beta-minus, β+ beta-plus, and electron capture. A beta-minus β– particle is an electron. (example Co60) A γ ray is a photon (note the A or Z do not change in this type of decay, go from excited state to a lower energy state). Question: What happens to Z and A in beta decay processes ?

Clicker question on alpha decay Which kinds of unstable nuclei typically decay by emitting an α particle? A. those with too many neutrons B. those with too many protons C. those with too many neutrons and too many protons D. Misleading question—the numbers of neutrons and protons in a nucleus are unrelated to whether or not it emits an alpha particle. Answer: C

A. those with too many neutrons B. those with too many protons Q43.3 Which kinds of unstable nuclei typically decay by emitting an alpha particle? A. those with too many neutrons B. those with too many protons C. those with too many neutrons and too many protons D. Misleading question—the numbers of neutrons and protons in a nucleus are unrelated to whether or not it emits an alpha particle. Answer: C

Nuclear stability and radioactivity Figure 43.4 (right) is a Segrè chart showing N versus Z for stable nuclides. In α decay, Z decreases by 2 and A decreases by 4, moving the nuclei closer to the line of stability.

Uranium decay chart Note the α decay and β decays in the chain

Clicker question on β emission Which kinds of unstable nuclei typically decay by emitting an electron? A. those with too many neutrons B. those with too many protons C. those with too many neutrons and too many protons D. Misleading question—the numbers of neutrons and protons in a nucleus are unrelated to whether or not it emits an electron. Answer: B

A. those with too many neutrons B. those with too many protons Q43.4 Which kinds of unstable nuclei typically decay by emitting an electron? A. those with too many neutrons B. those with too many protons C. those with too many neutrons and too many protons D. Misleading question—the numbers of neutrons and protons in a nucleus are unrelated to whether or not it emits an electron. Answer: B

Which kinds of unstable nuclei typically decay by emitting a γ ray ? Q43.5 Which kinds of unstable nuclei typically decay by emitting a γ ray ? A. those with too many neutrons B. those with too many protons C. those with too many neutrons and too many protons D. Misleading question—the numbers of neutrons and protons in a nucleus are unrelated to whether or not it emits gamma rays. Answer: D

A. those with too many neutrons B. those with too many protons Q43.5 Which kinds of unstable nuclei typically decay by emitting a gamma-ray photon? A. those with too many neutrons B. those with too many protons C. those with too many neutrons and too many protons D. Misleading question—the numbers of neutrons and protons in a nucleus are unrelated to whether or not it emits gamma rays. Answer: D

Radioactive decay law Here N(t) is the number of radioactive nuclei present. The quantity λ is the “decay constant” and determines the probability per unit time that a nuclei will decay. Question: How do we integrate this ? Question: What is the solution ?

Radioactive decay law What is the half-life ? This corresponds to N(t)/N0=1/2

Summary: Activities and half-lives The half-life is the time for the number of radioactive nuclei to decrease to one-half of their original number. The number of remaining nuclei decreases exponentially with decay constant λ (see Figure on the right). Activity is measured in either Curies (US) or Becquerel (Europe or Japan) 1 Ci= 3.7 x 1010Bq =3.7 x 1010decays/sec

Clicker question on radioactive decay law As a sample of radioactive material decays, the decay rate A. is directly proportional to the half-life and directly proportional to the number of radioactive nuclei remaining. B. is directly proportional to the half-life and inversely proportional to the number of radioactive nuclei remaining. C. is inversely proportional to the half-life and directly proportional to the number of radioactive nuclei remaining. D. is inversely proportional to the half-life and inversely proportional to the number of radioactive nuclei remaining. Answer: C

Clicker question on radioactive decay law As a sample of radioactive material decays, the decay rate A. is directly proportional to the half-life and directly proportional to the number of radioactive nuclei remaining. B. is directly proportional to the half-life and inversely proportional to the number of radioactive nuclei remaining. C. is inversely proportional to the half-life and directly proportional to the number of radioactive nuclei remaining. D. is inversely proportional to the half-life and inversely proportional to the number of radioactive nuclei remaining. Answer: C

Why does nuclear fusion of hydrogen require high temperatures? A. Positive charges repel each other. B. The nuclear force only acts at short range. C. both A. and B. D. neither A. nor B. Answer: C

Why does nuclear fusion of hydrogen require high temperatures? A. Positive charges repel each other. B. The nuclear force only acts at short range. C. both A. and B. D. neither A. nor B. Answer: C