When charcoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegrations of ¹⁴C per gram per minute. A sample from an ancient piece of charcoal shows ¹⁴C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of ¹⁴C is 5730 y.

Question

Philoid · Accepted Answer

Given, activity

Initial activity

Half-life of ¹⁴C

Disintegration rate

According to Law of Radioactivity,

No. of radioactive sample at time t,

∴

So,

Taking ln on both sides, we get

⇒

So,

⇒

When charcoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegrations of 14C per gram per minute. A sample from an ancient piece of charcoal shows 14C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of 14C is 5730 y.