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Lecture Two

# Atoms, Elements, and Isotopes

Reading: (Optional) pp 23-26 in Christiansen and Hamblin

Atoms (which have a typical size of 10-8cm)} consist of a nucleus (size 10-13cm) made of protons (p) and neutrons (n), surrounded by electrons. Protons have a positive electric charge and a mass of about 10-27 grams. Neutrons have no charge and weigh about the same as a proton. Electrons (e-) have a negative charge and a mass about 1,000 times smaller than that of protons or neutrons. The number of protons in the nucleus determines the number of electrons and hence the chemical type of the atom, e.g.,

1p=H, 2p+2n=He, 6p+6n=C, 7p+7n=N, 8p+8n=O, etc.

An element consists of all atoms a particular type. For example, carbon is an element, and so is hydrogen.

### Isotopes

Elements can have a variable number of neutrons in their nucleus. For example,

6p+6n=12C, 6p+7n=13C, 6p+8n=14C

are isotopes of carbon.

Nuclei with too few or too many neutrons are unstable and will decay with a characteristic timescale called the half life. The result of the decay is a different element. For example

14C --> 14N

half-life equal to 5740 years

### Isotopic Anomalies

Typical samples of material contain different isotopes in a particular ratio. For example, the hydrogen in water is predominantly 1H, with a small fraction of 2H and an even smaller fraction of 3H. The decay of a radioactive isotope in a closed environment such as a crystal can skew the abundance of the resulting isotope. For example, 40Ar is generally exceedingly rare. However the decay

40K --> 40Ar

in a crystal will produce an isotopic anomaly (too much 40Ar).

# Where Stuff Comes From

## General Considerations

We have just seen that matter (``stuff'') consists of atoms made of protons and neutrons (in the nucleus) and electrons. Adding or subtracting electrons from an atom will not change the chemical properties of the material. To do that, one has to change the number of protons in the nucleus. This is difficult to do, since protons are positively charged, and the nucleus is small! It can be done if one is willing to put enough energy into it.

## The Big Bang

### (Big Bang Nucleosynthesis)

Nature did so just after the big bang, when the universe was small and hot. The result was the elements

1H, 2H=D, 3He, and 4He

Calculations show that the mass fraction (MHe/MH) should be between 20 and 30%. Young stars are seen to have a helium mass fraction in this range, suggesting that helium did in fact form in the big bang. ( See ``The First Three Minutes'' by Steven Weinberg)

## Stellar Nucleosynthesis

The interiors of stars are also hot. The temperature at the center of the sun has been measured in the last few years using helioseismology. This works the same way seismology on the earth does, using sound waves (earthquakes) to probe the interior of the earth. The result is that the temperature of the sun's core is roughly 13,000,000K (or C, it doesn't much matter). This is hot enough to ram protons together in various ways, eventually resulting in the formation of helium, and the release of energy. However, the sun will never get hot enough to produce any heavier nuclei.

## Massive Stars

Stars more massive than the sun necessarily have higher temperature cores. Such stars can fuse three helium nuclei together to form carbon:

4He + 4He --> 8Be
4He + 8Be --> 12C

In very massive stars, further reactions produce all the elements up to iron (Fe).

## Supernovae

There is still the problem of getting the stuff out of the center of these massive stars. Observations tell us how it happens: massive stars explode, spilling their guts into space. We had a recent example of such an event in the Large Magellenic Cloud, supernova 1987A. During these violent explosions the temperature goes so high that elements beyond iron, such as uranium and other unstable elements are formed. These elements were detected in the debris of 1987A. Click here to see Supernova 1987a, courtesy of the Space Telescope Science Institute.

## Stardust

Essentially everything you see around you, and you yourself, are primarily stardust (the hydrogen in you is from the big bang---you contain no helium). Your constituent atoms were assembled long ago in the core of some massive star and ejected back into space in the violence of a forgotten supernova.

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