a
(a) \(\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^n}\)

==> \(\frac{1}{{16}} = {\left( {\frac{1}{2}} \right)^4} = {\left( {\frac{1}{2}} \right)^n}\)

==>\( n = 4.\)

Also \(n = \frac{t}{{{T_{1/2}}}}\)

==> \({T_{1/2}} = \frac{{40}}{4} = 10\,days\)