4. Radium-226 has a half-life of 1620 years. If a lab contains a 25 mg sample:
a) determine a formula to represent the amount present after t years.
b) determine the quantity present after 1000 years.
c) determine when 7 grams will remain.
a) The formula to represent the amount present after t years can be derived using the half-life formula:
A(t) = A0 * (1/2)^(t / t1/2)
Where:
A(t) is the amount present after t years
A0 is the initial amount (25 mg in this case)
t1/2 is the half-life (1620 years)
b) To determine the quantity present after 1000 years, substitute t = 1000 into the formula:
A(1000) = 25 * (1/2)^(1000 / 1620)
c) To determine when 7 grams will remain, set A(t) = 7 and solve for t:
7 = 25 * (1/2)^(t / 1620)