Half Life EQ: How is the half-life of a radioactive element used to determine how much of a sample is left after a given period of time?

What is “half-life?” The time taken for the radioactivity of a specified isotope to fall to half of its original value A radioactive material will have some nuclei (plural for nucleus) that are stable and some that are unstable. Stable nuclei – don’t change Unstable nuclei – will change into stable nuclei at different rates depending on the material.

The “speed” of half-life Some unstable nuclei will change quickly. For example, Lithium-8 has a half-life of 0.85 seconds Some unstable nuclei will change slowly. For example, uranium-238 has a half-life of 4.51 BILLION years. It’s important to remember that “half-life” is an amount of time.

An analogy You have 8 markers. Every minute you give away HALF your markers. After 1 MINUTE (or one half-life) you only have 4 markers left. After 2 MINUTES (or two half-lives) you have 2 markers left. After 3 MINUTES (or three half-lives) you have 1 marker left. Each “half-life” period, your total markers cuts in half. This is an example of how “half-life” works.

How half-life is used… just a few examples Radioactive dating Scientists use Carbon-14 to date materials, assisting them in a variety of areas. The formation of the earth The geologic timeline Fossil Dating Pharmacy How long a particular drug remains in your system

Sample Problem #1 If 100.0 grams of carbon-14 decays until only 25.0 grams of carbon is left after 11,460 years, what is the half life of carbon-14?

Step 1: List the “Given” and “Unknown” Values Initial Mass of the Sample – 100g Final Mass of the Sample – 25g Total time of decay – 11,460 years Unknown: Number of half lives = ? Half lives Half life = ? years

Step 2: Write down the equation relating half life, the number of half lives, and the decay time. Step 2(B): Rearrange it to solve for half life. Step 2 Total time of decay = number of half lives x (number of years/half life) Step 2(B) (Number of Years/Half life) = (total time of decay/number of half lives)

Step 3: Calculate how many half lives have passed during the decay of the sample. Fraction of the sample remaining = final mass/initial mass In this example: 25/100 = ¼ Therefore: 2 half lives have passed because ½ + ½ = ¼

Step 4: Calculate the half life Equation: Number of years/half life In this example: 11,460 years/2 half lives Therefore: Carbon-14’s half life is 5730 years

Sample Problem #2 Thallium-208 has a half-life of 3.053 minutes. How long will it take for 120g to decay to 7.5g?

Step 1: List the “given” and “unknown” values Half life – 3.053 minutes Initial Mass – 120g Final Mass – 7.5g Unknown Number of half lives = ? Half lives Total time of decay

Step 2: Write down the equation relating half life, the number of half lives, and the decay time, and then rearrange it to solve for the total time of decay. Total time of decay = number of half lives X (number of minutes/half life)

Step 3: Calculate how many half lives have passed during the decay of the given sample. Fraction of the sample remaining = 7.5g/120g 0.0625 = 1/16 Therefore: 4 half lives have passed because ½ + ½ + ½ + ½ = 1/16

Step 4: Calculate the total time required for the radioactive decay. Equation: Total time of decay = number of half lives x (number of minutes/half life) In this example: Total time of decay = 4 half lives X (3.053 min/half life) Therefore: Total time of decay = 12.21 minutes

Sample Problem #3 Gold-198 has a half-life of 2.7 days. How much of a 96g sample of gold-198 will be left after 8.1 days?

Step 1: Identify the “given” and the “unknown” Half-life – 2.7 days Total time of decay – 8.1 days Initial Mass – 96g Unknown Number of half-lives = ? Half-lives Final Mass = ? g

Step 2: Write down the equation relating half-life, the number of half-lives, and the decay time, and then rearrange it to solve for the number of half-lives. Total time of decay = number of half-lives X (number of days/half life)

Step 3: Calculate how many half-lives have passed during the decay of the given sample. Number of half lives = 8.1 days/2.7 days = 3 half-lives

Step 4: Calculate how much of the sample will remain after 3 half lives. Final mass of the sample = initial mass of the sample X the fraction of the sample remaining Fraction of the sample remaining after 3 half lives = ½ + ½ + ½ = 1/8 Final mass of the sample = 96g X 1/8 = 12g

Practice Page Complete the nine practice problems in your journal. You may use these notes. You may work in groups. Raise your hand when you have completed the assignment to receive your stamp. WE WILL GO OVER THE ANSWERS after you make an attempt at completing them on your own.

Web Reference http://webcheck-test.eharcourtschool.com/hrwfw/INT-D-bck/http/sh/hk6_0030390966/teacher/osp/data/chap09/sec1/math_skills2.pdf