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

Answer:

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

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

$N(t) = N_{0} e^{\frac{-0.693t}{t1/2}$

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

$15 = 120e^{\frac{-0.693t}{5730}} \\\\ln\frac{15}{120} = -0.693t/5730\\\\t = 17194 years$