The half-life of an isotope is 1000 years. A 50-gram sample of the isotope is sealed in a box. Homework Help ✎
How much is left after 10,000 years?
How long will it take to reduce to 1% of the original amount?
How long will it take until all of the original sample of the isotope is gone? Support your answer.
Half-life means time in which half of the original 50 grams will remain.
y = abn
a is the initial value,
b is the multiplier (0.5 since we are working with a half-life),
n is the number of thousands of years, and
y is the amount of the isotope that remains (in grams).
The equation is y = 50(0.5)x. Substitute 10 for x.
Use the equation below, where x is the number of years.
Use the equation from the help for part (a).
In this case, y = 1% of 50 and you are solving for x.
≈ 6600 years