Question

The half-life of radium is $1600$ years. What is the fraction of sample undecayed after $6400$ years?

• A. $\frac{1}{16}$
• B. $\frac{1}{4}$
• C. $\frac{1}{8}$
• D. $\frac{1}{24}$

Answer 1

Answer: (A)

$\frac{1}{16}$

Answer 2

Half-life, T = 1600 years Time of decay, t = 6400 years Number of half-lives, $n=\frac{t}{T}=\frac{6400}{1600}=4$ Fraction undecayed $=\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{n}=\left(\frac{1}{2}\right)^{4}=\frac{1}{16}$