Half Life

Half Life

High School

​

Learning Objectives

• Define half-life and its relationship to the process of radioactive decay.

• Differentiate between a nuclear reaction and a chemical reaction.

• Determine the amount of a radioactive substance remaining after a specific time.

• Calculate the half-life of a radioactive sample using provided data.

Key Vocabulary

​

Half-Life

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

​

Radioactive Decay

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

​

Nuclear Reaction

A reaction involving a change in an atom's nucleus, affecting its protons or neutrons.

​

Radiation

Energy or particles released from the nucleus of a radioactive atom during its decay process.

​

​

Chemical vs. Nuclear Reactions

Chemical Reactions

• ​These reactions involve the rearrangement of electrons surrounding an atom's nucleus.

• ​​The identity of the atoms does not change during the reaction.

• ​An example is iron reacting with oxygen to form rust.

Nuclear Reactions

• ​These reactions involve changes within the nucleus, affecting protons and neutrons.

• ​​Atoms can be transformed into atoms of a different element.

• ​Radioactive decay, like Carbon-¹⁴ becoming Nitrogen-¹⁴, is an example.

​

Solved Example 1
The half-life of Carbon-14 is 5730 years. How much of an original 100g sample will remain after 17,190 years?

​

Step 1: Analyze and Sketch the Problem

​

Solved Example 1
The half-life of Carbon-14 is 5730 years. How much of an original 100g sample will remain after 17,190 years?

​

Step 2: Solve for the Unknown

​

Solved Example 1
The half-life of Carbon-14 is 5730 years. How much of an original 100g sample will remain after 17,190 years?

​

Step 3: Evaluate the Answer

• After 1 half-life (5,730 years), 50g would remain.

• After 2 half-lives (11,460 years), 25g would remain.

• After 3 half-lives (17,190 years), 12.5g would remain.

• The answer is consistent with the step-by-step decay.

Multiple Choice

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

• A chemical reaction releases radiation, while a nuclear reaction forms new molecules.

• There is no difference; both terms describe the same process.

• A nuclear reaction involves changes in the nucleus of an atom, while a chemical reaction involves the electrons.

• Nuclear reactions involve forming rust, while chemical reactions involve atomic decay.

​

​

Understanding Half-Life

• Half-life is the time for half of a radioactive sample’s nuclei to decay.

• A shorter half-life means an isotope is less stable and more radioactive.

• Uranium-235 is more radioactive than uranium-238 because its half-life is shorter.

• Half-life describes the statistical behavior of many atoms, not a single one.

​

Multiple Choice

Which statement most accurately describes the concept of half-life?

• It allows for the precise prediction of when a single, specific atom will undergo decay.

• It is the total time it takes for a radioactive sample to become completely stable.

• It is the time it takes for half of the unstable nuclei in a sample to decay and is a constant property for that isotope.

• All radioactive isotopes share the same half-life value.

​

​

Calculating with Half-Life

​

Multiple Choice

If a sample of a radioactive isotope undergoes two half-lives, what percentage of the original parent isotope is left?

• 50%

• 25%

• 12.5%

• 0%

​

Common Misconceptions About Half-Life

Misconception	Correction
A substance is gone after two half-lives.	After two half-lives, 25% of the substance still remains.
All radioisotopes have the same half-life.	Each radioactive isotope has its own unique half-life.
Half-life predicts when a single atom will decay.	It's a statistical average for a large group of atoms.

Multiple Choice

The half-life of Iodine-131 is 8 days. If a hospital starts with a 40-gram sample, how much Iodine-131 will remain after 24 days?

• 20 grams

• 10 grams

• 5 grams

• 2.5 grams

Multiple Choice

Uranium-²³⁸ has a half-life of 4.47 billion years, while protactinium-²³³ has a half-life of 27 days. What does this difference imply about their stability?

• Protactinium-²³³ is more stable than Uranium-²³⁸.

• Stability cannot be determined from half-life.

• Uranium-²³⁸ is more stable than protactinium-²³³.

• Both isotopes are equally stable.

Multiple Choice

A scientist finds a rock and a Geiger counter shows its radioactivity has dropped to 1/8th of its original level. If the isotope's half-life is 2 million years, what is the estimated age of the rock?

• 2 million years old

• 4 million years old

• 6 million years old

• 8 million years old

Multiple Choice

Using the formula $$A = n(\frac{1}{2})^{\frac{t}{T_{\frac{1}{2}}}}$$ , calculate the final amount 'A' of a radioactive substance if the time elapsed 't' is exactly three times the half-life 'T_½', and the initial amount 'n' is 100g.

• 50g would remain.

• 6.25g would remain.

• 12.5g would remain.

• 25g would remain.

​

Summary

Poll

On a scale of 1-4, how confident are you about calculating the remaining amount of a substance using its half-life?

• 1

• 2

• 3

• 4