The rate of disintegration of a radio active element at time t is proportional to its mass at that time. Then the time during which the original mass of 1 5 gm . will disintegrate into its mass of 0.5 gm . is proportional to

Step-by-step solution

(C) Let m be the mass of the radioactive element at time t . Then the rate of disintegration is dm dt which is proportional to m . dm dt m dm dt =- km , where k >0 dm m =- kdt 1 ~m dm =- k dt + c m =- kt + c Initially, i.e. when t =0, ~m =1.5 (1.5)=- k 0+ c c = ( 3 2 ) m =- kt + ( 3 2 ) m - 3 2 =- kt ( 2 m 3 )=-k t When m =0.5= 1 2 , then aligned & ( 2 1 2 3 )=- kt ( 1 3 )=- kt - 3=- kt & t= 1 k 3 aligned Thus required time is proportional to 3 .