Question

directions: label all your answers.

1. during transmutation (radioactive decay) the daughter atom % + parent atom % must equal __________%
2. during transmutation the atoms of the original radioactive element are the parent | daughter atom.
3. during transmutation the daughter atom is stable | unstable and the parent atom is stable | unstable

figure 1

number of half-lives	0	1	2	3	4	5
% of original parent atoms	100	50	25	12.5	6.25	3.125
age of element xc	0 hrs	2 hrs	4 hrs	6 hrs	8 hrs	10 hrs
age of element bz	0 days	15 days	30 days	45 days	60 days	75 days
age of element qs	0 m.y.	3 m.y.	6 m.y.	9 m.y.	12 m.y.	15 m.y.

let’s say element xc is radioactive parent that decays to a stable daughter element vx. it has a half-life age of 2 hours.

1. figure 1: how old is element xc after 3 of its half lives? __________
2. figure 1: what percent of element xc is left after 3 of its half lives? __________
3. figure 1: what percent of the daughter element vx is present after 3 of parent xc’s half lives? __________

let’s say element bz is radioactive parent that decays to a stable daughter element cc. it has a half-life age of 15 days.

1. figure 1: how old is element bz after 2 of its half lives? ________ after 5 half lives? ________
2. figure 1: what percent of element bz is left after 5 of its half lives? __________

let’s say element qs is radioactive parent that decays to a stable daughter element aq. it has a half-life age of 3 million years.

1. figure 1: how old is element qs if 25% of the original of qs is present? __________
2. figure 1: what is the ratio of parent atoms to daughter atoms at 2 half-lives of qs:

parent %= ________% & daughter %=________

Explanation:

Step1: Answer basic transmutation rules

1. Total parent + daughter = 100%
2. Original atoms = parent atoms
3. Parent = unstable, daughter = stable

Step2: Extract Xc data from table

1. 3 half-lives = 6 hrs
2. 3 half-lives: 12.5% parent left
3. Daughter % = $100 - 12.5 = 87.5$

Step3: Extract Bz data from table

1. 2 half-lives = 30 days; 5 half-lives =75 days
2. 5 half-lives: 3.125% parent left

Step4: Extract Qs data from table

1. 25% parent = 2 half-lives =6 m.y.
2. 2 half-lives: 25% parent, $100-25=75$% daughter

Answer:

1. 100
2. PARENT
3. STABLE; UNSTABLE
4. 6 hrs
5. 12.5
6. 87.5
7. 30 days; 75 days
8. 3.125
9. 6 m.y.
10. Parent %=25; Daughter %=75