By the definction of half life we know that it represents the time after which the number of original atoms is reduced to half. Hence after one half life the number remaining is 1/2 of the original number. Thus after two half lives, the active remaining number will be (1/2) x 1/2 of the original number. Proceeding with the same argument the active remaining number of atoms after four half lives will be 1/2 x 1/2 x 1/2 x 1/2 of the original number i.e.