Radioactive plutonium−239 (t1/2 = 2.44 × 105 yr) is used in nuclear reactors and atomic bombs. If there are 6.40 × 102 g of the isotope in a small atomic bomb, how long will it take for the substance to decay to 1.00 × 102 g, too small an amount for an effective bomb? (Hint: Radioactive decays follow first-order kinetics.)

Explanation:

Expression for rate law for first order kinetics is given by:

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process  

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

b) for g of the isotope to decay to  

The time for g of the isotope to decay to   is

pv=nrt

explanation: