Question

A radioactive isotope, 14C decays to become 14N. After a time period of about 6,000 years, only about 12.5% of an original sample of 14C remains. The remainder has decayed to 14N. According to this information, approximately how long is one half-life of 14C?

Answer 1

2000 years

Step-by-step explanation:

A radioactive molecule will continuously decay and turn into another molecule. This nature of the radioactive molecule makes them can be used to estimate the age of an object. Half-life is the unit of time needed for radioactive molecules to decay to half of its mass. The formula for the mass remaining will be:

`N(t)= N_(0) ((1)/(2))^{(t)/(t_(1/2) ) }`

Where

N(t)= number of the molecule remains

N0= number of molecule initially

t= time elapsed

t1/2= half time

We have all variable besides the half time, the calculation will be:

`N(t)= N_(0) ((1)/(2))^{(t)/(t_(1/2) ) }`

`0.125= 1 ((1)/(2))^{(6000)/(t_(1/2) ) }`

`((1)/(8))= ((1)/(2))^{(6000)/(t_(1/2) ) }`

`((1)/(2))^3= ((1)/(2))^{(6000)/(t_(1/2) ) }`

3= 6000/ (t1/2)

t1/2= 6000/3= 2000

The half-life is 2000 years