Question

The half life of carbon-14 is 5,730 years. ABOUT how old is a sample that has one-fourth of its carbon-14 unchanged?

a.10,000 years

b.15,100 years

c.11,400 years

d.5,700 years

Answer 1

C. 11400 years.

Step-by-step explanation:

The time constant of the isotope is:

`\tau = (5730\,yr)/(\ln 2)`

`\tau = 8266.643\,yr`

The decay of the isotope is described by the following model:

`(m(t))/(m_(o)) = e^{-(t)/(\tau) }`

`-(t)/(\tau) = \ln (m(t))/(m_(o))`

`t = -\tau \cdot \ln (m(t))/(m_(o))`

`t = -(8266.643\,yr)\cdot \ln \left((1)/(4) \right)`

`t \approx 11460.001\,yr`

The right answer is C.