Question

The half life of radioactive element is 5 yrs. the fraction of the radioactive substance that remians after 20 years is ?

Answer 1

 All the Radioactive activity follows first order kinetics
Half life , t1/2=t50% decomposed = 5 yrs

  t1/2=0.693/k
                       where, k= rate constant

now,  k= 0.693/5 = 0.1386 yrs⁻¹                 

according to first order reaction,

t = {2.303log[R₀]/[R]}/k      where ,  [R₀]= initial amount
                                                          [R] = amount left
                                                           t= time 

20= {2.303log[R₀]/[R]}/0.1386 s

⇒ log[R₀]/[R] = {20Х01386}/2.303=2.772/2.303 =1.2

 [R₀]/[R]=  antilog(1.2) = 15.8 

 So, [R]/[R₀] = 1/15.8 = 0.063  ans.