Q: Which equation correctly calculates the fraction of a radioisotope remaining after $n$ half-lives?

$\text{Fraction remaining} = \frac{1}{2^n}$

Question 1

A radioactive isotope has a half-life of $8$ days. If you start with $160$ mg of the isotope, how much will remain after $24$ days?

Accepted Answer

$20$ 	ext{ mg}$

Question 2

The half-life of Iodine-131 is $8.021$ days. What percentage of a sample remains after $40.11$ days?

Accepted Answer

$42.1\%$

Question 3

A hospital receives a $100$ mg sample of arsenic-74, which has a half-life of $18$ days. How much arsenic-74 remains after $72$ days?

Accepted Answer

$6.25$ 	ext{ mg}$

Question 4

Sodium-24, used in medical diagnostics, has a half-life of $15$ days. What percentage of a sample remains after $30$ days?

Accepted Answer

$25\%$

Question 5

Which of the following best describes a radioisotope?

Accepted Answer

A version of an element with an unstable nucleus that emits radiation as it decays.

Question 6

If a sample of a radioisotope decays to $1/8$ of its original amount, how many half-lives have passed?

Accepted Answer

$3$

Question 7

A $0.325$ mol sample of $\mathrm{CO}_2$ is placed in a $5.0$ L reaction vessel. After $4$ half-lives, what is the concentration of $\mathrm{CO}_2$?

Accepted Answer

$0.026$ 	ext{ M}$

Question 8

A graph shows that $50\%$ of a radioisotope remains after $10$ days. What is the half-life of the isotope?

Accepted Answer

$10$ 	ext{ days}$

Question 9

Which equation correctly calculates the fraction of a radioisotope remaining after $n$ half-lives?

Accepted Answer

$	ext{Fraction remaining} = \frac{1}{2^n}$

Question 10

A patient is given a $200$ mg dose of a radioisotope with a half-life of $6$ hours. How much remains after $18$ hours?

Accepted Answer

$25$ 	ext{ mg}$

Question 11

If a radioisotope decays from $80$ g to $10$ g in $24$ days, what is its half-life?

Accepted Answer

$6$ 	ext{ days}$

Question 12

Which of the following statements about half-life is correct?

Accepted Answer

Half-life is the time required for half of the atoms in a sample to decay.

Question 13

A $50$ mg sample of a radioisotope decays to $6.25$ mg in $36$ hours. What is the half-life of the isotope?

Accepted Answer

$12$ 	ext{ hours}$

Question 14

A scientist needs at least $10\%$ of a radioisotope to remain for an experiment. If the half-life is $5$ days, what is the maximum number of days the experiment can last before the sample falls below $10\%$?

Accepted Answer

$16.6$ 	ext{ days}$

Question 15

If a radioisotope has a half-life of $3$ years, what fraction of the original sample remains after $9$ years?

Accepted Answer

$\frac{1}{8}$

Question 16

A $10$ g sample of a radioisotope is left for $4$ half-lives. What is the final mass of the sample?

Accepted Answer

$0.625$ 	ext{ g}$

Question 17

Which of the following best explains why radioisotopes are useful in medical imaging?

Accepted Answer

They emit radiation that can be detected by specialized equipment, allowing tracking within the body.

Radioactive Decay and Half-Life in GOB Chemistry

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