Question

Carbon-14 has a half-life of 5,730 years. In how many years will 120 grams of Carbon-14 decay to 15 grams?

11,460 years
17,190 years
22, 920 years
28,650 years

Answer 1

120 grams of Carbon-14 decays to 15 grams in 17,190 years.

Answer 2

Time taken for the C-14 to decay from 120 to 15 g = 17194 years

Step-by-step explanation:

Given:

Half life of C-14, t1/2 = 5730 years

Initial amount of C-14, N(0) = 120 g

Amount of C-4 after time t , N(t) = 15 g

Formula:

Radioactive decay is given by the following expression

`N(t) = N_(0) e^{(-0.693t)/(t1/2)`

Substituting the values of N(t), N(0), t1/2 we get:

`15 = 120e^{(-0.693t)/(5730)} \\\\ln(15)/(120) = -0.693t/5730\\\\t = 17194 years`