Question

Archaeologists use the radioactive decay of carbon-14 to estimate the age of fossils and can be used on samples of bone, cloth, wood and plant fibers. The half-life of carbon-14 is 5,730 years. Several human bones have been unearthed at an archaeological dig. 25% of the original carbon-14 isotope is remaining and scientists estimate the bones to be ___________ years old.

Answer 1

The answer should be 11,460 because the first half-life leaves 50 percent left and the next half-life would leave 25 percent which dates the bones at 11,460 years old.

Answer 2

Answer:

The age of bones was estimated to be 11,462 years old.

Explanation:

Formula used :

$N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}$

where,

$N_o$ = initial mass of isotope

N = mass of the parent isotope left after the time, (t)

$t_{\frac{1}{2}}$ = half life of the isotope

$\lambda$ = decay constant

We have:

$N_o$ = x, N = 25% of x = 0.25 x

t = ? .$t_{1/2}=5,730 years$

$\lambda=\frac{0.693}{5,730 years}=0.000120942 year^{-1}$

Now put all the given values in this formula, we get

$0.25x=x\times e^{-0.000120942 year^{-1}\times t}$

t = 11,462.4338 years ≈ 11,462 years

The age of bones was estimated to be 11,462 years old.