The isotope 239 Pu 94 has a half life of 24,400 years. If a sample of nuclear waste originally contained 12kg of 239 Pu 94, how much time must pass before the amount falls to 3 kg?

Equation for half-lives:Nt = No x (1/2)^nNo = initial amountNt = final amount after t yearsn = number of half lives = t/(single half-life)t = yearsNt = 3/12 = 0.25No = 12/12 = 1.00n = t/(24400)3/12 = (12/12) x (0.5)^(t/24400)(0.25) = 1.00 x (0.5)^(t/24400)0.25/1.00 = 0.5^(t/24400)ln(0.25) = ln(0.5^(t/24400))ln(0.25) = (t/24400)*ln(0.5)ln(0.25)/ln(0.5) = (t/24400)2 = t/244002*24400 = tt = 48800 yrsanswer is t = 48,800 yrs