Question

Half life of a radioactive sample is $2x$ years. What fraction of this sample will remain undecayed after $x$ years?

• A. $\frac{1}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{\sqrt{3}}$
• D. $2$

Answer 1

Answer: (B)

$\frac{1}{\sqrt{2}}$

$\lambda =\frac{2.303}{t}\log \left(\frac{N_0}{N}\right)$
$\frac{0.693}{t_{1/2}}=\frac{2.303}{t}{\log }_{10}\left(\frac{N_0}{N}\right)$
$\frac{0.693}{2x}=\frac{2.303}{x}{\log }_{10}\left(\frac{N_0}{N}\right)$
$\frac{1}{2}{\log }_{10}2=\log \left(\frac{N_0}{N}\right)$
$\frac{N}{N_0}=\frac{1}{\sqrt{2}}$
Fraction of sample undecayed $=\frac{1}{\sqrt{2}}$