As the amount of radioactive isotope remaining after 2 hrs is 1/16 of the intial amount,the eauation N=(N)initial x (exp(-kt)), here k denote lambda, takes the form N)initial/16=N)initial x (exp(-kt)) i.e., exp(-kt)=1/16 => -kt= log(1/16) .....[taking log on both the sides] =>-kt=-4log2 now time taken is 2 hrs therfore, 2k=4log2 => k=2log2 now half life =log2/k=1/2hrs=30 mins ,hence the answer (ii) THIS WAS FOR NCERT TRADITIONAL WORMS NEXT SOLUTION IS A BETTER APPROACH the amount left after n-half lives=initial amount/(2 raised to power n),now as the final amount 1/16 ,i.e., 1/(2 raised to power 4) of the initial amount, 4 half lives have passed therefore, 4(half life)=2 hrs => half life=30 min

The half life of a radioactive substance is 10 days. This means that 7/8 part of the mass of the substance disintegrates in 30 days

The half-life of a radioactive substance depends upon the strength of the nuclear force between the nucleons of its atoms

the rate of disintegration is proportional to number of radioactive atoms present initially in source