## Half-life Calculations Worksheet With Answers

Half-life calculations can be a challenging concept for many students to grasp. However, with practice and repetition, this topic can be mastered. In this worksheet, we will provide examples of half-life calculations and provide answers to help you better understand this concept. By the end of this worksheet, you should feel confident in your ability to calculate half-life values for different substances.

### Introduction to Half-life Calculations

Half-life is a term used to describe the time it takes for half of a substance to decay or transform into another substance. This concept is commonly used in nuclear physics, chemistry, and biology to determine the stability and decay of radioactive isotopes. Understanding half-life calculations is essential for predicting the behavior of these isotopes over time.

### Basic Half-life Calculations

To calculate the half-life of a substance, you need to know the initial quantity of the substance, the time it takes for half of the substance to decay, and the rate of decay. The formula for calculating half-life is:

Half-life = (time taken for half of the substance to decay) / (rate of decay)

For example, if a substance has an initial quantity of 100 grams and it takes 10 days for 50 grams to decay, the half-life would be:

Half-life = 10 days / 50 grams = 0.2 days/gram

### Advanced Half-life Calculations

In more complex situations, you may need to calculate the half-life of a substance over multiple decay cycles. To do this, you can use the formula:

Final quantity = Initial quantity * (1/2)^n

Where n is the number of decay cycles. By rearranging this formula, you can solve for the half-life value:

Half-life = (time taken for half of the substance to decay) / (n)

For example, if a substance has an initial quantity of 100 grams and it takes 10 days for 25 grams to decay (after 2 decay cycles), the half-life would be:

Half-life = 10 days / 2 cycles = 5 days/cycle

### Half-life Calculations Worksheet

Now that we have covered the basics of half-life calculations, let’s try some practice problems to test your understanding. Below are a series of questions along with their answers to help you practice calculating half-life values for different substances.

#### Question 1:

A radioactive substance has an initial quantity of 200 grams. If it takes 20 days for 50 grams to decay, what is the half-life of the substance?

Answer: Half-life = 20 days / 50 grams = 0.4 days/gram

#### Question 2:

A radioactive isotope undergoes two decay cycles. If the initial quantity is 150 grams and it takes 30 days for 37.5 grams to decay, what is the half-life of the isotope?

Answer: Half-life = 30 days / 2 cycles = 15 days/cycle

#### Question 3:

A radioactive element has an initial quantity of 300 grams. After three decay cycles, only 37.5 grams remain. If each cycle takes 10 days, what is the half-life of the element?

Answer: Half-life = 10 days / 3 cycles = 3.33 days/cycle

### Conclusion

Half-life calculations can be challenging but with practice and repetition, you can master this concept. By understanding the formulas and principles behind half-life calculations, you will be able to predict the decay and stability of radioactive isotopes with confidence. Use this worksheet as a tool to improve your skills in calculating half-life values and continue to practice until you feel comfortable with this topic.