NetNews Usenet Archive 1993 #3/NN_1993_3.iso/spool/sci/chem/5911

Text File | 1993-01-21 | 1.5 KB | 51 lines

Newsgroups: sci.chem
Path: sparky!uunet!usc!sdd.hp.com!news.cs.indiana.edu!babbage.ece.uc.edu!ucunix.san.uc.edu!roberts
From: [e-mail] (Michael Alan Roberts)
Subject: Est. the age of rock
Message-ID: <[e-mail]>
Organization: University of Cincinnati
Date: Thu, 21 Jan 1993 19:46:08 GMT
Lines: 41

To the person who wanted to know how to estimate the age of a rock based
on radioisotope decay:

The logic goes something like this: After one half-life, only 50% of the
original non-decayed material remains. If 25% of the non-decayed
material is left, then, obviously, two half-lives have elapsed.

In your example, 10% of the material remains. The number of half-lives
that have elapsed can be defined as "x", where:

(1/2)^x = 0.1

Solving:

x * log(0.5) = log(0.1)
x = log(0.1)/log(0.5)
x = -1 / -0.30103
x = 3.3219 half-lives
Since one half-life is stated as 1.3 billion years in your problem, the
age of the rock can be estimated as:

3.3219 half-lives * 1.3 billion yrs./half-life = 4.3185 billion years.

Mind you, you will have to correct the math to account for whatever
number of significant figures you were given.

Also note that the general expression for the number of half-lives that
have elapsed, er, sorry, the expression for the age of an object based
on radioactive decay is:

h * log(p) / log(0.5)

where h is the duration of one half-life, and p is the proportion (NOT
the percentage) of non-decayed material remaining.

Hope this helps.

Michael Roberts
University of Cincinnati
[e-mail]