Question

If a sample originally had 410 atoms of carbon-14, how many atoms will remain after 16,110 years?

Answer 1

58.4 atoms

Step-by-step explanation:

To find the remaining amount of atoms, you need to use the half-life formula:

`A = A_0*((1)/(2))^{(t)/(h)`

In this formula,

-----> A = remaining amount (atoms)

-----> A₀ = initial amount (atoms)

-----> t = time passed (years)

-----> h = half-life (years)

The half-life is the amount of time that needs to pass for the initial amount of a substance to decay by 50% (or 1/2). According to the graph, 50% of the initial substance is left after 5,730 years.

A = ? atoms t = 16,110 years

A₀ = 410 atoms h = 5,730 years

`A = A_0*((1)/(2))^{(t)/(h)` <----- Half-life formula

`A = 410*((1)/(2))^{(16,110)/(5,730)` <----- Insert values

`A = 410*((1)/(2))^{2.81` <----- Divide 16,110 by 5,730

`A = 410*0.142` <----- Raise
`(1)/(2)` to 2.81

`A = 58.4` <-----Multiply 410 and 0.142