Question

The isotope known as carbon-14 is radioactive and will decay into the stable form nitrogen-14. As long as an organism is alive, it ingests air, and the level of carbon-14 in the organism remains the same. When it dies, it no longer absorbs carbon-14 from the air, and the carbon-14 in the organism decays. The half-life of carbon-14 is 5770 years. Assume an organic sample is 14,000 years old. How many half-lives is 14,000 years?

Answer 1

Answer:

The number of half lives in 14000 years is  2.4258.

Step-by-step explanation:

Initial amount of carbon-14 =$N_o$

Final amount of carbon-14= N

Half life of carbon-14 = $t_{1/2}=5770 year$

Decay constant = k = $\frac{0.693}{t_{1/2}}=\frac{0.693}{5770 year}$

Age of the sample = t = 14,000 years

$N=N_o\times e^{-kt}$

$N=N_o\times e^{-\frac{0.693}{5770 year}\times 14,000 yeras}$

$N=N_o\times 0.1861$

Formula used for number of half lives

$N=\frac{N_o}{2^n}$

where,

N= amount of reactant left after n-half lives

$N_o$ = Initial amount of the reactant

n = number of half lives

$N_o\times 0.1861=\frac{N_o}{2^n}$

$2^n=\frac{1}{0.1861}$

$2^n=5.3734$

Taking log both sides

$n\log 2=\log (5.3734)$

n = 2.4258

The number of half lives in 14000 years is  2.4258.