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Nuclei

Question

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

$\frac{1}{16}$

$\frac{1}{4}$

$\frac{1}{8}$

$\frac{1}{24}$

Solution

A.

$\frac{1}{16}$

Half-life T = 1600 years

Time of decay t = 6400 years

Number of half-lives

n = $\frac{t}{T}$

= $\frac{6400}{1600}$

n = 4

Fraction undeecayed = $\frac{N}{N_{0}}$

= ${(\frac{1}{2})}^{n}$

= ${(\frac{1}{2})}^{4}$

Fraction undeecayed = $\frac{1}{16}$

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