A 5.00 g charcoal sample from an ancient fire pit has a activity of 63.0 disintegrations per minute. A living tree has a activity of 15.3 disintegrations per minute per gram. The half-life of is 5730 y. We have to find how old the charcoal sample is.

Solution:             Click For PDF Version

Let be the number of nuclides in a 5.00 g piece of wood before it became a piece of charcoal.

A living tree has a activity of 15.3 disintegrations per minute per gram. Therefore, the activity in 5.00 g piece of wood at time t earlier would have been

.

The present activity measured in the piece of charcoal, , is 63.0 disintegrations per minute.

We know that variation of disintegration rates with time is given as

.

We therefore note that

The half-life of is 5730 y. Its disintegration constant will be

Therefore, the age of the piece of charcoal will be