A radioactive substance decays to 1/16th of its initial activity in 40 days. The half life of  radioactive substance expressed in days is

From Rutherford and Soddy law for radioactive decayN=N0e-λtwhere N0 and N are number of atom in a radioactive substance at time t = 0 and t = t and ,λ is decay constant.Also half-life T1/2=0.693λ∴NN0=e0.693-T1/2tGiven, t = 40 days, NN0=116∴116=e-0.693 x 40T1/2⇒0.693 x 40T1/2=log 16T1/2=0.693 x 40log 16=9.99≃10 days