A radioisotope is place near a radiation detector, which registers 80 counts per second. Eight hours later, the detector registers five counts per section. What is the isotope's half-life?

The isotopes half life is 2 hours

Since given the following:

time = 8 hours * 3600s/hr = 28800 seconds

A₀ = 80 Bq as the first registration of detector counts per second

A = 5 Bq as the registration of detector counts per second eight hours later

Using the formula:

∴ A = A₀ e^-λt

∴ A/A₀ = e^-λt

∴ ln (A/A₀) = - λt

∴ λ = - ln (A/A₀) / t = ln2 / t_{1/2}

∴ t_{1/2} = - ln2 / ln (A/A₀) (t)

∴ t_{1/2} = - ln2 / ln (5/80) (8 hours) = 2 hours