Question

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?

Answer 1

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