Half-Life

Half-Life

High School

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Learning Objectives

• Define half-life and its significance in the process of radioactive decay.

• Distinguish between a chemical reaction and a nuclear reaction.

• Determine an isotope's half-life from decay data or a graph.

• Calculate the amount of radioactive sample remaining after a specific time.

Key Vocabulary

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Half-Life

The specific time interval during which half of the nuclei in a radioactive sample have decayed.

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Radioactive Decay

The process where an unstable nucleus loses energy by emitting radiation to become more stable.

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Nuclear Reaction

A reaction that changes an atom's nucleus, affecting the number of its protons or neutrons.

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Chemical Reaction

A process that rearranges the electron structures of atoms, without changing the atom's nuclei.

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Chemical vs. Nuclear Reactions

• A chemical reaction involves changes in the arrangement of an atom’s electrons.

• The nucleus is unchanged, like when iron reacts with oxygen to form rust.

• A nuclear reaction is a fundamental change that occurs within an atom's nucleus.

• This alters protons or neutrons, like ¹⁴C decaying into ¹⁴N.

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Solved Example 1
Carbon-14 has a half-life of 5730 years. If you start with a 144g sample, how much will remain after 17,190 years?

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Step 1: Analyze and Sketch the Problem

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Solved Example 1
Carbon-14 has a half-life of 5730 years. If you start with a 144g sample, how much will remain after 17,190 years?

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Step 2: Solve for the Unknown

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Solved Example 1
Carbon-14 has a half-life of 5730 years. If you start with a 144g sample, how much will remain after 17,190 years?

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Step 3: Evaluate the Answer

Multiple Choice

What is the primary difference between a nuclear reaction and a chemical reaction?

• Nuclear reactions create new elements, while chemical reactions only form new compounds.

• Nuclear reactions involve changes in the nucleus, while chemical reactions involve electrons.

• Both reactions involve changes to the nucleus, but on different scales.

• Chemical reactions change the nucleus, while nuclear reactions change the electron arrangement.

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What Is Radioactive Decay?

• Unstable atomic nuclei decay due to an unbalanced number of protons and neutrons.

• During decay, the nucleus emits radiation as particles or high-energy gamma rays.

• This is a natural process that stops when the nucleus becomes stable.

• It has important uses in radiotherapy and medical imaging.

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Multiple Choice

Why does radioactive decay occur?

• It happens when an atom gains extra electrons in its outer shell.

• It is artificially stimulated in all cases to release energy.

• It occurs when an atom has an unstable nucleus with unbalanced forces.

• It is a result of a chemical reaction between two different atoms.

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What is Half-Life?

• Half-life (T_1/2) is the time for half of a radioactive sample to decay.

• ​It is a property that measures the stability of a radioactive isotope.

• An isotope with a short half-life decays quickly and is more radioactive.

• For example, ²³⁵U is more radioactive than ²³⁸U due to its shorter half-life.

Multiple Choice

Which of the following best defines half-life?

• The time it takes for half of the nuclei in a radioactive sample to decay.

• Half the total lifespan of a radioactive isotope.

• The measure of how much radiation is emitted by a sample in one second.

• The time required for an entire radioactive sample to decay completely.

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Calculating with Half-Life

Multiple Choice

If a sample of a radioactive isotope has a half-life of 10 years, how much of a 100g sample will be left after 20 years?

• 0g

• 25g

• 50g

• 12.5g

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Common Misconceptions About Radioactive Decay

Misconception	Correction
A radioactive element is gone after two half-lives.	After two half-lives, 25% of the original radioactive material still remains.
We can predict exactly when a specific atom will decay.	Radioactive decay is a random process for a single atom.
All radioisotopes decay at the same rate.	Each isotope has its own unique and constant half-life.
After one half-life, the mass of the sample is halved.	The total mass of the sample changes very little.

Multiple Choice

Uranium²³⁸ has a half-life of 4.47 billion years, and uranium²³⁵ has a half-life of 0.704 billion years. Which isotope is considered more radioactive and why?

• Uranium²³⁵, because it has a smaller atomic mass.

• Uranium²³⁸, because it is more stable.

• Uranium²³⁸, because it has a longer half-life.

• Uranium²³⁵, because it decays at a faster rate.

Multiple Choice

If a lab analysis shows that only one-fourth (25%) of the original carbon-14 in a fossil is remaining, how many half-lives has it undergone?

• 2 half-lives

• 3 half-lives

• 1 half-life

• 4 half-lives

Multiple Choice

The half-life of Element X is 2 years. If you start with a 160g sample, how much of Element X will remain after 8 years?

• 10g

• 40g

• 20g

• 5g

Multiple Choice

After 24.0 days, 2.00 milligrams of an original 128.0 milligram sample remain. What is the half-life of the sample?

• 3.0 days

• 6.0 days

• 8.0 days

• 4.0 days

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Summary

Poll

On a scale of 1-4, how confident are you about the concepts covered in today's review?

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