Respuesta :
Answer:
The number of half lives in 14000 years is 2.4258.
Step-by-step explanation:
Initial amount of carbon-14 =[tex] N_o[/tex]
Final amount of carbon-14= N
Half life of carbon-14 = [tex]t_{1/2}=5770 year[/tex]
Decay constant = k = [tex]\frac{0.693}{t_{1/2}}=\frac{0.693}{5770 year}[/tex]
Age of the sample = t = 14,000 years
[tex]N=N_o\times e^{-kt}[/tex]
[tex]N=N_o\times e^{-\frac{0.693}{5770 year}\times 14,000 yeras}[/tex]
[tex]N=N_o\times 0.1861[/tex]
Formula used for number of half lives
[tex]N=\frac{N_o}{2^n}[/tex]
where,
N= amount of reactant left after n-half lives
[tex]N_o[/tex] = Initial amount of the reactant
n = number of half lives
[tex]N_o\times 0.1861=\frac{N_o}{2^n}[/tex]
[tex]2^n=\frac{1}{0.1861}[/tex]
[tex]2^n=5.3734[/tex]
Taking log both sides
[tex]n\log 2=\log (5.3734)[/tex]
n = 2.4258
The number of half lives in 14000 years is 2.4258.
