Question

Radon-222 has a half-life of $3.8$ days. If one starts with $0.064kg$ of Radon-222, the quantity of Radon-222 lefts after $19$ days will be

• A. $0.02kg$
• B. $0.62kg$
• C. $0.032kg$
• D. $0.024kg$

Answer 1

Answer: (A)

$0.02kg$

Number of half-lives, $n=\frac{19}{3.8}=5$

After every half-life, number of Radon-222 is halved. Hence, quantity of Radon-222 after $n-$ half lives is:

$\frac{N}{N_o}={\left(\frac{1}{2}\right)}^n$

$N=0.064\times {\left(\frac{1}{2}\right)}^5$

$N=0.02kg$