$A$ radioactive substance decomposes such that after $100 \ min$,its concentration becomes $1/8$ of the original concentration. Calculate the rate constant $(k)$ and half-life time $(t_{1/2})$.

• A
  $k = 2.08 \times 10^{-2} \ min^{-1}, t_{1/2} = 33.3 \ min$
• B
  $k = 1.04 \times 10^{-2} \ min^{-1}, t_{1/2} = 66.6 \ min$
• C
  $k = 2.08 \times 10^{-2} \ min^{-1}, t_{1/2} = 16.6 \ min$
• D
  $k = 4.16 \times 10^{-2} \ min^{-1}, t_{1/2} = 33.3 \ min$