# How to do carbon dating math

Suppose a linen sample of 1 gram is analysed in a counter.

## dating checklist men - How to do carbon dating math

In the previous article, we saw that light attenuation obeys an exponential law.

To show this, we needed to make one critical assumption: that for a thin enough slice of matter, the proportion of light getting through the slice was proportional to the thickness of the slice.

This question can be answered using a little bit of calculus. Once we have an expression for t, a "definite integral" will give us the mean value of t (this is how "mean value" is defined).

From the equation above, taking logarithms of both sides we see that lt = -ln(N/N.

This is because there is carbon dioxide (CO exchange, and so the ratio of C-14 to the far more common carbon isotope, C-12, will begin to decrease as the C-14 atoms decay, yielding nitrogen (N-14) with the emission of an electron (or "beta particle") plus an anti-neutrino.

The ratio of C-14 to C-12 in the atmosphere's carbon dioxide molecules is about 1.3×10, and this value is assumed constant for the main part of archaeological history since the formation of the earth's atmosphere.

In his article Light Attenuation and Exponential Laws in the last issue of Plus, Ian Garbett discussed the phenomenon of light attenuation, one of the many physical phenomena in which the exponential function crops up.

In this second article he describes the phenomenon of radioactive decay, which also obeys an exponential law, and explains how this information allows us to carbon-date artefacts such as the Dead Sea Scrolls.

Let's look further at the technique behind the work that led to Libby being awarded a Nobel prize in 1960.

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