The a half-life of 5,715 years.After 2,000 years, a sample of the isotope is reduced to 1.2 grams.What was the initial size of the sample (in grams)? How much will
Remain after 20,000 years (i.e., after another 18000 years)? Round your answers to four decimal
Places.
A)1.0706 , 0.0947
B)2.4471 , 0.2164
C)1.5294 , 0.1352
D)2.1412 , 0.1893
E)1.9883 , 0.1758

Question

The  a half-life of 5,715 years.After 2,000 years, a sample of the isotope is reduced to 1.2 grams.What was the initial size of the sample (in grams)? How much will
Remain after 20,000 years (i.e., after another 18000 years)? Round your answers to four decimal
Places.
A)1.0706 , 0.0947 
B)2.4471 , 0.2164 
C)1.5294 , 0.1352 
D)2.1412 , 0.1893 
E)1.9883 , 0.1758

Quizplus · Accepted Answer

Let's use the formula for radioactive decay:

A = A0 * (1/2)^(t/T)

where A is the amount remaining after time t, A0 is the initial amount, T is the half-life, and (^) means to raise to a power.

For the first question, we know that after 2,000 years, the amount remaining is 1.2 grams. We also know the half-life is 5,715 years. So we can plug in these values and solve for A0:

1.2 = A0 * (1/2)^(2000/5715)

1.2 / (1/2)^(2000/5715) = A0

A0 = 1.5294 grams

For the second question, we need to find the amount remaining after another 18,000 years. So we can use the same formula, but with t = 20,000 years (since we already accounted for 2,000 years in the previous calculation):

A = A0 * (1/2)^(20000/5715)

A = 0.1352 grams (rounded to four decimal places)

Therefore, the answer is C.

The a Half-Life of 5,715 Years