ESS C109/C209: Isotope Geochemistry

Lecture 2 Notes

Introduction to Isotope Geochemistry

April 4, 2007

Introduction

The parts of an atom. Nomenclature for nuclear chemistry

p+ (= H⁺) = ¹₁H⁺

n = ¹₀n

e– = b–

Other things that interact with nuclei (created or destroyed in nuclear reactions)

a = ⁴₂He has mass, charge (typically), and energy

e+ = b+ has energy and charge but little mass

Photon = g has energy but no mass or charge

Neutrino = n_e etc. has energy but no mass or charge

Exotic particles (muons, etc.)

Hand out Nuclides & Isotopes booklets

Nuclear Chemistry

1. Neutrons and protons interact to create nuclear chemistry.
1. Analogous to the electron-nucleus (electronic) interactions in chemistry
2. Some nuclear structures are stable (e.g., ⁴₂He)
   Stability determined by nuclear binding energy
   E=mc² – Low energy (stable) nuclei are less massive. 1 amu=931.5 MeV
   
   Binding energy of ⁴₂He:
   
   Mass of ⁴₂He = 4.00260325 amu
   
   Mass of 2 ¹₁H = 2 x 1.007825032
   Mass of 2 ¹₀n = 2 x 1.008664923
   Total = 4.03297991
   
   Binding energy = 0.030377 amu = 28.3 MeV
   
   
3. Is a neutron more stable than ¹₁H?

i. Less stable nuclei decay to more stable nuclei

ii. Most common mechanisms are a or b emission, or fission.

4. Table 15 (p. 27) – Binding energies vs. mass.
   
   
1. Why are some nuclei more stable than others? (Table 14 (p. 27) )
1. Protons are like-charge, tend to repel

i. Too many protons à unstable

2. Neutrons dilute charge, bind protons together

i. More protons à more neutrons

ii. Nonlinear – more neutrons per proton in heavy nuclei.

3. Neutrons & protons like to “pair up”

i. Even # of protons = more stable

ii. Even # of neutrons = more stable

iii. For light elements, same # protons & neutrons = more stable

1. Even-Even nuclei most stable

2. Can you find any stable odd-odd nuclei?
Odd-Odd nuclei only stable for light elements
(when # protons = # neutrons)

4. Shell structure: “Noble nuclei”

i. In chemistry, some elements are particularly stable in atomic form – which ones? (He, Ne, Ar, Kr, Xe)

1. Stable because they have full electronic shells, i.e. 2 s-electrons, 6 p-electrons, etc. in each orbital.

ii. There are nuclear-chemical shells also, nuclei with full shells of either protons or neutrons are particularly stable, or “magic”.

1. Magic numbers are 2, 8, 20, 28, 50, 82, 126, 184

2. Look at calcium in booklet. See the magic number?

3. A nucleus with a magic number of neutrons and a magic number of protons is “doubly magic”.

5. Return to Table 15 (p. 27). Why is ⁴₂He so stable?
   
   
2. Modes of decay on unstable nuclei
1. b-decay (⁴⁰₁₉K, p. 46) Students write equations.

i. Too many protons? b+ -decay (where’s it go?)

ii. Too many neutrons? b- -decay (where’s it go?)

2. Electron capture (e) – similar to b+ -decay
3. a-decay (⁸₄Be, p. 40)

i. emission of ⁴₂He

ii. most common for nuclei beyond mass 140

4. Spontaneous fission (²⁴⁴₉₄Pu, p. 71)

i. Splitting yields two daughters of similar mass (~1/2 parent mass).

ii. Daughters are typically heterogenous (many different products).

iii. Most common for very heavy nuclei (m > 200)

iv. Usually accompanied by many short-lived b- decays to regain line of stability.