Question

A sample contains $10^{- 2} \, kg$ each of the two substances $A$ and $B$ with half-lives $4 \, s$ and $8 \, s$ respectively. Their atomic weights are in the ratio of $1:2$ . Amounts of $A$ and $B$ after an interval $16 \, s$ are

• A. $A=0.625\times 10^{- 4 }kg,B=0.25\times 10^{- 3 }kg$
• B. $A=0.25\times 10^{- 3 }kg,B=0.625\times 10^{- 4 }kg$
• C. $A=2.5\times 10^{- 3 }kg,B=6.25\times 10^{- 4 }kg$
• D. $A=6.25\times 10^{- 4 }kg,B=2.5\times 10^{- 3 }kg$

Answer 1

Answer: (D)

The amount left after $N$ half - lives
$N=N_{0}\left[\frac{1}{2}\right]^{n}$
For A,
$n=\frac{t}{T_{\frac{1}{2}}}=\frac{16 s}{4 s}=4$
$N_{A}=10^{- 2}kg\left[\frac{1}{2}\right]^{4}=6.25\times 10^{- 4}kg$
For B,
$n=\frac{16 s}{8 s}=2$
$N_{B}=10^{- 2}kg\left[\frac{1}{2}\right]^{2}=2.5\times 10^{- 3}kg$