Question

The fraction of atoms of radioactive element that decays in $6$ days is $7/8$. The fraction that decays in $10$ days will be

• A. $\frac{77}{88}$
• B. $\frac{71}{80}$
• C. $\frac{31}{32}$
• D. $\frac{15}{16}$

Answer 1

The correct option is C $\frac{31}{32}$

fraction left undecayed is $1-\left(7/8\right)=1/8$.

Decay constant, $\lambda =\frac{{\log }_e\left(8\right)}{6}=3.466\times {10}^{-1}perday$

Fraction left undecayed is $exp\left(-3.466\times {10}^{-1}\times 10\right)=exp(-3.466)\approx 1/32$

So fraction decayed is $1-\frac{1}{32}=\frac{31}{32}$