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

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

Step-by-step explanation:

Formula used :

`N=N_o* e^(-\lambda t)\\\\\lambda =\frac{0.693}{t_{(1)/(2)}}`

where,

`N_o` = initial mass of isotope

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

`t_{(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=(0.693)/(5,730 years)=0.000120942 year^(-1)`

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

`0.25x=x* e^{-0.000120942 year^(-1)* t}`

t = 11,462.4338 years ≈ 11,462 years

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