Discussion Forum

Half-lives of two radioactive elements A and b are 20 min and 40min respectively. Initially, the samples have an equal number of nuclei. After 80min. the ratio of decayed number of A and B nuclei will be

Answer:

Explanation:

A: number left

                   $N\rightarrow \frac{N}{2}\rightarrow\frac{N}{4}\rightarrow\frac{N}{8}\rightarrow\frac{N}{16}$

Numer decayed

    $N_{A}=N-\frac{N}{16}=\frac{15}{16}N$

B: Numers left :  $N\rightarrow \frac{N}{2}\rightarrow\frac{N}{4}$

Numers decayed

   $N_{B}=N -\frac{N}{4}=\frac{3}{4}N$

Ratio:   $\frac{N_{A}}{N_{B}}=\frac{(15/16)N}{(3/4)N}=\frac{5}{4}$