Question

A piece of cloth is dated using carbon-14. The cloth is determined to be 1400 years old. The half-life of C-14 is 5730 years. The C-14 radioactivity in the cloth will be ________ the radioactivity in a new cloth.

Answer 1

84.4 %

Step-by-step explanation:

Let the activity of carbon is dN / dt.

Us ethe law of radioactivity

`dN/dt= e^(-\lambda t)`

Where, λ is decay constant and t be the time

λ = 0.6931 / T

Where, T be the halflife

λ = 0.6931 / 5730 per year

λt = 0.6931 x 1400 / 5730 = 0.1693

`dN/dt= e^(-0.1693)`

dN/dt = 0.844

it becomes 84.4%.