a) A well preserved piece of wood found at an archaeological site has 43 % of the carbon-14 that it must have had when it was living. Using the fact that carbon-14 has a half-life of 5700 years, calculate the age (in years) of this piece of wood.

b) A different piece of wood is found to have 9 % of the carbon-14 that it must have had when it was living. Calculate its age (in years) and enter it in the box below.

Question

contestada

Respuesta :

kobenhavn kobenhavn · Answer 1 · 2019-10-11T12:18:45+02:00

Answer: a) 7034 years

b) 20070 years

Explanation:

Expression for rate law for first order kinetics is given by:

[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant = 100

a - x = amount left after decay process

Given half life = 5700 years

[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]

[tex]5700years=\frac{0.693}{k}[/tex]

[tex]k=0.00012years^{-1}[/tex]

a) 43 % of carbon-14

[tex]t=\frac{2.303}{0.00012}\log\frac{100}{43}[/tex]

[tex]t=7034years[/tex]

Thus the age of this piece of wood is 7034 years

b) 9 % of the carbon-14

[tex]t=\frac{2.303}{0.00012}\log\frac{100}{9}[/tex]

[tex]t=20070years[/tex]

Thus the age of this piece of wood is 20070 years