question_answer

If 80% of a radioactive element undergoing decay is left over after a certain period of time t from the start, how many such periods should elapse from the start for just over 50% of the element to be left over?

A) 1                                 

B) 2                     

C) 3       

D) 4

Correct Answer: C

Solution :

[c] Let \[a=100,\] \[(a-x)=80\] (Amount left). \[\therefore \] Amount left \[=\frac{a}{{{(2)}^{n}}}\] [n = number of half lives] \[80=\frac{100}{{{(2)}^{n}}}\Rightarrow {{(2)}^{n}}=\frac{10}{8}\] \[\therefore \,\,\,n\,\,\log 2=\log 10-3\log 2=1-3\times 0.3=0.1\] \[n=\frac{0.1}{\log 2}=\frac{0.1}{0.3}=\frac{1}{3}.\]   Alternatively