c
(c) Fraction remains after \(n\) half lives

\(\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^n} = {\left( {\frac{1}{2}} \right)^{t/T}}\)

\(\therefore\) \(\frac{N}{{{N_0}}} = {\left( {\frac{1}{2}} \right)^{\frac{{T/2}}{T}}} = {\left( {\frac{1}{2}} \right)^{1/2}} = \frac{1}{{\sqrt 2 }}\)