Balancing Nuclear Equations & Calculating Half-Life West Valley High School General Chemistry Mr. Mata

Balancing Nuclear Equations Step 1: Add atomic masses & atomic numbers on each side of equation. Step 2: Balance atomic masses & atomic numbers to find the atomic mass & atomic number of the unknown particle. Step 3: Determine the unknown symbol by using the atomic number.

Example 1 1 H + 3 H -> ? 1 1 1 H + 3 H -> 4 He 1 1 2

Example 2 9 Be + 1 H -> ? + 4 He 4 1 2 9 Be + 1 H -> 6 Li + 4 He 4 1 2 9 Be + 1 H -> 6 Li + 4 He 4 1 3 2

Example 3 42 K -> 0 e + ? 19 -1 42 K -> 0 e + 42 Ca 19 -1 20

Calculating Half-Life A radioisotope has a half-life of 4 days. How much of a 20 gram sample would remain at the end of each time period? Known: t ½ = 4 days 20 gram sample Unknown: amount left after each half-life

Problem 1 Solution 4 days 4 days 4 days 4 days 20 g 10 g 5 g 2.5 g 1.25 g

Calculating Half-Life 2. The mass of cobalt-60 is found to have decreased from 0.800 grams to 0.200 grams in a period of 10.5 years. Calculate the half-life of cobalt-60. Known: 0.800 g -> 0.200 g decrease in 10.5 yrs Unknown: t ½ cobalt-60

Problem 2 Solution 0.800 g 0.400 g 0.200 g 10.5 years 5.25 yr 5.25 yr 0.800 g 0.400 g 0.200 g 10.5 years t ½ cobalt-60 = 5.25 years

Calculating Half-Life 3. Carbon-14 emits beta radiation and decays with half-life of 5730 years. Assume you start with a mass of 2 grams of carbon-14. How long is three half-lives? How many grams of the isotope remain at the end of three half-lives? Known: t ½ = 5730 years 2 grams Unknown: How long is three half-lives? How much after three half-lives?

Problem 3 Solution 3 t ½ = 3 (5730 years) = 17,190 years 5730 yrs 5730 yrs 5730 yrs 2 g 1 g 0.5 g 0.25 g