Question

The half-life of the carbon-14 isotope is about 5700 years. It occurs naturally in all organic matter. Scientists have discovered that the charcoal from a tree burned in a volcanic eruption contains 35% of the isotope level that is normally found in living trees. How many years ago did the volcanic eruption occur

Answer 1

Answer:

The volcanic eruption occurred 8,634.90 years ago.

Step-by-step 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 = x

N = mass of the parent isotope left after the time, (t) = 35% of x=0.35x

$t_{\frac{1}{2}}$ = half life of the isotope = 5700 year

$\lambda$ = rate constant

$0.35x=x\times e^{-(\frac{0.693}{5700 years})\times t}$

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

$t=8,634.90 years$

The volcanic eruption occurred 8,634.90 years ago.