In the year 2005, a picture supposedly painted by a famous artist some time after 1635 but before 1685 contains 95.4 percent of its carbon-14 (half-life 5730 years).

Question

From this information, could this picture have been painted by this artist?  

Approximately how old is the painting? 

Answer 1

Hi Koosi,

This is the classic carbon dating question.

1. To begin, the equation for carbon dating is as follows: Nf = Nt*e^(-0.693t/k).
2. Where Nf is the final value, Nt is the original or total value, t is the time, and k is is the half-life.
3. Performing mathematical transposition, one ends up with the following equation:
4. t = (k*ln(Nf/Nt)/(-0.693)
5. Plugging the provided numbers into this equation, one gets 424 years.
6. Subtracting 424 from 2005, the year the painting was made in was 1581. So no, the painting could not have been made between 1635-1685.