in order to decrease radioactive nuclei to one million of its initial number,number of half lives required is

Dear Student,
For the firrst order of chemcial kinetics,
t=2.303log(a/a-x)/l
=>t=2.303log(a/a-10⁶)/l
no of half lives=t/t_1/2=(2.303log(a/a-10⁶)/l)/(0.693/l) (since t_1/2=0.693/l)
no of half lives can be found by substituting a which is the initial number that is not given in the question.