An archaeologist graduate student found a leg bone of a large animal during the building of...

Radioactive decay follows first-order kinetics. By measuring the C-14 activity of a dead sample, its age can be calculated using the expression for radioactive decay as:

where is its age, is the decay constant of C-14, is the C-14 activity in a fresh sample of the species, is its C-14 activity at present.

Given, = 14.8 dpm/g (dpm/g is disintegration per minute per gram)

= 15.3 dpm/g

Half-life of carbon-14, = 5760 years

= 0.693 / (5760 years) = 1.203*10^-4 years^-1

Substituting these values in the equation ,

Age   = [ 2.303/(1.203*10^-4 years^-1) ] * log (15.3 dpm/g / 14.8 dpm/g)

= [ 2.303/(1.203*10^-4) ] * log (15.3/14.8) years

= 19143.807 * 0.0144 years

= 275.67 years

Hence the bone is 275 years old.

The correct option is option e - 275 years.