Two radioactive nuclei P and Q , in a given sample decay into a stable nucleus R . At time t = 0 , the number of P species are 4 N 0 and that of Q is N 0 . The half-life of P (for conversion to R ) is 1 minute whereas that of Q is 2 minutes . Initially, there are no nuclei of R present in the sample. When the number of nuclei of P and Q is equal, the number of nuclei of R present in the sample would be

Step-by-step solution

P Q No. of nuclei, at t = 0 4 N 0 N 0 Half-life 1 min 2 min No. of nuclei after N P N Q time t Let after t min, the number of nuclei of P and Q are equal. ∴ N P = 4 N 0 1 2 t / 1 and N Q = N 0 1 2 t / 2 As N P   =   N Q ∴ 4 N 0 1 2 t / 1 = N 0 1 2 t / 2 4 2 t / 1 = 1 2 t / 2 or 4 = 2 t 2 t / 2 or 4   =   2 t / 2       o r     2 2   =   2 t / 2 or t 2 = 2 or t = 4   min After 4   minutes , both P and Q have an equal number of nuclei. &there