Question

A 25g sample of Carbon-14 decays until 3.125g of the radioactive isotope

remains. How old is the sample in years?

Answer 1

The sample age = 17,190 years

Further explanation

The atomic nucleus can experience decay into 2 particles or more due to the instability of its atomic nucleus.

Usually radioactive elements have an unstable atomic nucleus.

The main particles are emitted by radioactive elements so that they generally decay are alpha (α), beta (β) and gamma (γ) particles

General formulas used in decay:

`\large{\boxed{\bold{N_t=N_0((1)/(2))^{t/t(1)/(2) }}}`

t = duration of decay

t 1/2 = half-life

N₀ = the number of initial radioactive atoms

Nt = the number of radioactive atoms left after decaying during T time

It is assumed that the half life of carbon is 14 = 5730 years

t1/2 = 5730 years

Nt=3.125 g

No=25 g

`\tt 3.125=25(1)/(2)^(t/5730)\\\\0.125=(1)/(2)^(t/5730)\\\\(1)/(2)^3=(1)/(2)^(t/5730)\\\\3=t/5730\rightarrow t=17,190~years`