Question

How much of the parent isotope would be remaining after 7 half-lives have passed?

a. 6.25 %
b. 1.56 %
c. 0.78 %
d. 0.39 %
If a radioactive element has a half-life of 425 years, how old would a rock be that only had 3.125 % of the parent isotope remaining?
a. 2125 years
b. 1700 years
c. 2550 years
d. 3400 years
Based on your graph above, approximately how much of the parent isotope would be remaining after 3.5 half-lives?
a. 16 %
b. 12 %
c. 4 %
d. 8 %
Based on your graph above, approximately how many half-lives have passed when only 35 % of the parent isotope is remaining?
a. 0.75
b. 1.5
c. 2.1
d. 2.5"

Answer 1

After 7 half-lives, 0.78% of the parent isotope would be remaining. A rock with 3.125% of the parent isotope remaining would be approximately 2125 years old. After 3.5 half-lives, approximately 12.5% of the parent isotope would be remaining. When only 35% of the parent isotope is remaining, approximately 2.5 half-lives have passed.

The Answer is :

Option C.

Option A.

Option B.

Step-by-step explanation:

The amount of parent isotope remaining after 7 half-lives can be calculated by repeatedly dividing the initial amount by 2. After 7 half-lives, the remaining fraction is (1/2)^7 = 1/128 = 0.0078. This is equivalent to 0.78% (option c).

To determine the age of a rock with 3.125% of the parent isotope remaining, we can use the same formula. Setting up the equation (1/2)^n = 0.03125, we find that n is approximately 5. This means 5 half-lives have passed, which corresponds to 5 x 425 years = 2125 years (option a).

Based on the graph, after 3.5 half-lives, approximately 12.5% of the parent isotope would be remaining (option b).

Similarly, when only 35% of the parent isotope is remaining, approximately 2.5 half-lives have passed (option d).