Question

A “new” painting supposedly painted by Michelangelo (1475–1564) is authenticated by C-14 dating. The C-14 content (t1/2 = 5730 y) of the canvas is 0.972 times that of a living plant. Could the painting have been done by Michelangelo, or at least while Michelangelo was alive?

Answer 1

Radioactive decay follows first order kinetics and the rate law is

k = [2.303/t] log a /a-x where t= time

a = initial concentration (intial activity)

a-x = concentraion at timet (activity at time t )

Given initial activity = activity of living plant = 1

activity of sample at t= 0.972

rate constant k = 0.693/ half life

= 0.693/5730 yr^-1

thus substituting all the values

0.693/5730 yr^-1 = [2.303 / t ] log 1/0.972

thus time t= 234.86 yr

Thus the painting was done in [2017 - 234.86 =]1782.14 which is not the life time of Michalangelo.

thus it was fake paining, not done by Michelangelo.