Radioactive gold-198 is used in the diagnosis of liver problems. the half-life of this isotope is 2.7 days. if you begin with a sample of 8.1 mg of the isotope, how much of this sample remains after 2.6 days?

See explanation below

Explanation:

To solve this problem, we need to use the expression of half life decay of concentration (or mass) which is the following:

m = m₀e^-kt  (1)

In this case, k will be the constant rate of this element. This is calculated using the following expression:

k = ln2/t₁/₂  (2)

Let's calculate the value of k first:

k = ln2/2.7 = 0.2567 d⁻¹

Now, we can use the expression (1) to calculate the remaining mass:

m = 8.1 * e^(-0.2567 * 2.6)

m = 8.1 * e^(-0.6674)

m = 8.1 * 0.51303

m = 4.16 mg remaining