Question

0.1 g atom of radioactive isotope ${}_Z^{A}X$(half-life 5 days) is taken. How many number of atoms will decay during eleventh day.

• A. $=1.926\times {10}^{21}$ atom
• B. $=7.926\times {10}^{21}$ atom
• C. $=3.926\times {10}^{21}$ atom
• D. $=9.926\times {10}^{21}$ atom

Answer 1

The correct option is A $=1.926\times {10}^{21}$ atom

Amount left after 10 days = amount disintegrating on 11th day.
$\begin{array}{c}C=C_0{\left(\frac{1}{2}\right)}^y\\ =0.1{\left(\frac{1}{2}\right)}^2\end{array}]$ $y=\frac{totaltime}{t_{50}}=2$
$=0.1\times \frac{1}{4}$
$=0.025g$ atm after 10 days
Amount left on 11th day $(y=\frac{1}{5}half-life)$
When $C_0=0.025{\left(\frac{1}{5}\right)}^{1/5}$g atm
$=0.0218gatm$
Amount disintegeating on 11th day $=C_0-C$
$=0.025-0.0218$
$=3.2\times {10}^{-3}gatm$
$=1.926\times {10}^{21}atom$