Question

$80$% of the radioactive nuclei present in a sample are found to remain undecayed after one day. The percentage of undecayed nuclei left after two days will be____________.

• A. $64$
• B. $20$
• C. $46$
• D. $80$

Answer 1

The correct option is A $64$

$\lambda =\frac{2.303}{t}\log \left(\frac{N_0}{N}\right)$
$=\frac{2.303}{1}\log \left(\frac{100}{80}\right)$
$\lambda =\frac{2.303}{2}\log \left(\frac{100}{N}\right)$
$\frac{2.303}{1}\log \left(\frac{100}{80}\right)=\frac{2.303}{2}\log \left(\frac{100}{N}\right)$
${\left(\frac{5}{4}\right)}^2=\frac{100}{N}$
$N=64$