Question 1

A sample of carbon-14 has 25% of its original activity remaining. Given that the half-life of carbon-14 is $$5730$$ years, how old is the sample?

Accepted Answer

$$11,460$$ years

Question 2

Which of the following equations correctly represents the radioactive decay law?

Accepted Answer

$$N(t) = N_0$ e$$^{-kt}$$

Question 3

Which type of nuclear process is represented by the equation $$^A_ZX \$$rightarrow ^{A-4}$$_{Z-2}Y + ^4$_2He$$?

Accepted Answer

Alpha decay

Question 4

A radioactive isotope has a half-life of $$10$$ years. If you start with $$80$$ grams, how much will remain after $$30$$ years?

Accepted Answer

$$10$$ grams

Question 5

Which of the following statements best explains why uranium is used for dating rocks billions of years old?

Accepted Answer

Uranium has a very long half-life, allowing it to date ancient materials.

Question 6

Which nuclear process results in the emission of a positron?

Accepted Answer

Positron emission

Question 7

If a sample of $$^{56}Cr $$weighs $$110$$ grams, how much will remain after $$56$$ days if its half-life is $$28$$ days?

Accepted Answer

$$27.5$$ grams

Question 8

A medical facility uses $$500 mg of$$ $$^{24}Na ($$half-life $$15$$ hours) for a procedure. How much $$^{24}Na $$remains after $$45$$ hours?

Accepted Answer

$$62.5 mg$$

Question 9

Which of the following best describes the relationship between the number of radioactive atoms and time, as shown in a decay curve?

Accepted Answer

The number of atoms decreases exponentially over time.

Question 10

Which of the following is a correct generic equation for beta emission?

Accepted Answer

$$^A_ZX \rightarrow ^A$$_{Z+1}$$Y + ^0$_{-1}e$$

Question 11

A scientist finds a fossil with $$12.5\% of $$its original carbon-14 remaining. How many half-lives have passed?

Accepted Answer

3

Question 12

Which of the following is true about isotopes with short half-lives?

Accepted Answer

They decay quickly and are useful for dating recent events.

Question 13

Which nuclear process is represented by $$^A_ZX + ^0$_{-1}e \rightarrow ^A$$_{Z-1}$$Y$$?

Accepted Answer

Electron capture

Question 14

A radioactive sample decays from $$200$$ atoms to $$25$$ atoms in $$60$$ seconds. What is the half-life of the sample?

Accepted Answer

$$20$$ seconds

Question 15

Which of the following is a real-world application of radioactive isotopes with short half-lives?

Accepted Answer

Medical imaging and cancer treatment

Question 16

If a radioactive isotope has a half-life of $$5$$ days, what fraction of the original sample remains after $$15$$ days?

Accepted Answer

$$\frac{1}{8}$$

Question 17

Which of the following best describes spontaneous fission?

Accepted Answer

A heavy nucleus splits into two lighter nuclei and releases energy.

Question 18

A radioactive isotope decays to $$1/16 of $$its original amount in $$32$$ hours. What is its half-life?

Accepted Answer

$$8$$ hours

Question 19

Which of the following is NOT a type of radiation emitted during nuclear decay?

Accepted Answer

Photon absorption

Question 20

A balloon experiment models radioactive decay. If you start with $$20$$ balloons and have $$5$$ left after $$3$$ intervals, what is the approximate half-life in intervals?

Accepted Answer

1.5 intervals

Radioactive Decay, Half-Life, and Nuclear Processes worksheet

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