The half-life of carbon 14 is 5,730 years. How much would be left of an original 50-gram sample after 2,292 years

37.9g of carbon 14 remains

Explanation:

The radioactive decay of an atom follows the equation:

Ln[A] = -kt + Ln[A]₀

Where [A] is amount of isotope after time t, k is decay constant and [A]₀ initial amount of the isotope.

We can find k from half-life using:

k = ln 2 / Half-Life

k = ln 2 / 5730 years

k = 1.2097x10⁻⁴ yrs⁻¹

Replacing in the equation all values:

Ln[A] = -1.2097x10⁻⁴ yrs⁻¹*2292yrs + Ln[50g]

Ln[A] = 3.635

[A] = 37.9g of carbon 14 remains