A radio-active material is reduced to \(1 / 8\) of its original amount in \(3\) days. If \(8 \times 10^{-3}\,kg\) of the material is left after \(5\) days. The initial amount of the material is \(.......\,g\)

\(\frac{ N _0}{8}= N _0\left(\frac{1}{2}\right)^{ n }\)

\(n =3\)

\(3 \text { half lives }=3 \text { days }\)

\(1 \text { half life }=1 \text { day }\)

\(5 \text { days }=5 \text { half life }\)

\(N = N _0\left(\frac{1}{2}\right)^{ n }\)

\(8 \times 10^{-3}= N _0\left(\frac{1}{2}\right)^5\)

\(N _0=256 \times 10^{-3}\,kg\)

\(N _0=256\,g\)