Aim: What is the half-life of a radioisotope

• Do Now:1. 210 4

84 2_______Po He __________________________________

2. 8 85 4 _______B Be __________________________________

3. 14 06 1_______C e __________________________________

4. 15 158 7 ______O N __________________________________

5. 238 492 2_______U He ___________________________________

Stable and Unstable Nuclei

• Unstable nuclei spontaneously decay giving off rays and particles

• Stability of nucleus depends on neutron to proton ratio

• For elements with low atomic number (1-20)– Neutron/proton=1– Nucleus of isotope is stable

• For elements with high atomic number (82-83)– Neutron/proton = about 1.5– Stable isotope

Stable and Unstable Nuclei

Protons in the nucleus repel each other because of like charges. The binding energy holds the nucleus together.

Stable atoms have a strong binding energy Atoms with unstable nuclei have an imbalance

of energy in the nucleus Unstable atoms are constantly changing to

become more stable

Band of Stability

Transmutation

• In (natural) transmutation, the nucleus spontaneously decays into a new element.

• In artificial transmutation, the nucleus is first bombarded with high energy particles, then decays and changes into a new element.

Question

Half-Life

• Every radioisotope has a rate of decay.• Half-life is the time it takes for half of the

sample to decay into new elements.

Half-Life

Half-Life

• Table N lists half-life, decay mode (particles emitted during decay), nuclide (radioisotope, and name of nuclide.

• The half-life of Ra-226 is 1600 years; meaning, in 1600 years half of Ra-226 will decay, and in another 1600 years half of what was remaining will decay.

• After 3200 years, how many half-lives has Ra-226 gone through?

Half-Life Formula

Fraction Remaining

• has a half-life of 8.07 days. A 10 gram sample was allowed to decay for 32 days. What fraction will remain?

Fraction Remaining

• has a half-life of 8.07 days. A 10 gram sample was allowed to decay for 32 days. What fraction will remain?

Step 1: Use equation:

fraction remaining = n , n= # of half lives

Fraction Remaining

• has a half-life of 8.07 days. A 10 gram sample was allowed to decay for 32 days. What fraction will remain?

Step 2: Find n (# of half lives)n = n = n = 4

Fraction Remaining

• has a half-life of 8.07 days. A 10 gram sample was allowed to decay for 32 days. What fraction will remain?

Step 3: substitute 4 for n

fraction remaining = n

fraction remaining = 4 =

Half-life

• 100 grams of a radioisotope decayed to 12 ½ grams after 90.7 years. What was the half-life?

Half-life

• 100 grams of a radioisotope decayed to 12 ½ grams after 90.7 years. What was the half-life?

Step 1: Fid how many half-lives it took to go from 100 g to 12 ½ g

100 g 50 g 25 g 12 ½ g3 half-lives passed

Half-life

• 100 grams of a radioisotope decayed to 12 ½ grams after 90.7 years. What was the half-life?

Step 2; To find the half-life take the total time and divide by the number of half-lives.

Initial Amount (Original Amount)

• A radioisotope has a half-life of 10 days. 1 gram remains after 40 days. What was the initial amount of the radioisotope?

Initial Amount (Original Amount)

• A radioisotope has a half-life of 10 days. 1 gram remains after 40 days. What was the initial amount of the radioisotope?

Step 1: Find the number of half-lives passed.

n (# of half-lives) = n = n = 4

Initial Amount (Original Amount)

• A radioisotope has a half-life of 10 days. 1 gram remains after 40 days. What was the initial amount of the radioisotope?

Step 2: substitute 4 for n

fraction remaining = n

fraction remaining = 4 =

Initial Amount (Original Amount)

• A radioisotope has a half-life of 10 days. 1 gram remains after 40 days. What was the initial amount of the radioisotope?

Step 3: Find initial amount.1/16 of the original amount remains1 g = amount remaining1g = (1/16) x , x= initial amount

Questions

1. Which radioisotopes have the same decay mode and have half-lives greater than 1 hour?(1) Au-198 and N-16 (3) I-131 and P-32(2) Ca-37 and Fe-53 (4) Tc-99 and U-233

Questions

2. After decaying for 48 hours, 1/16 of the original mass of a radioisotope sample remains unchanged. What is the half-life of this radioisotope?(1) 3.0 h (3) 12 h(2) 9.6 h (4) 24 h