In a sample initially, there are an equal number of atoms of two radioactive isotopes A and B . 3 days later, the number of atoms of A is twice that of B . The half-life of B is 1.5 days. What is the half-life (in days) of isotope A ?

Step-by-step solution

A B t = 0 N 0 N 0 t 0 = 3   d a y s 2 N N 2 N = N 0 ( 0 . 5 ) t 0 / τ 1 N = N 0 ( 0 . 5 ) t 0 / τ 2 2 = (0.5) t 0 ( 1 τ 1 − 1 τ 2 ) 0.5 − 1 = ( 0.5 ) 3 τ 1 − 2 ⇒ - 1 = 3 τ 1 - 2                                     ∴ τ 1 = 3 days