The half-life of radium is approximately 1,600 years. If the present amount of radium in a certain location is 900 grams, how much will remain after 400 years? Express your answer to the nearest gram.
A)Q = 734 gram
B)Q = 768 gram
C)Q = 757 gram
D)Q = 752 gram
E)Q = 744 gram

Question

Quizplus · Accepted Answer

We can use the formula:

N(t) = N0*(1/2)^(t/half-life)

where N(t) is the amount remaining after time t, N0 is the initial amount, and half-life is the half-life of the substance.

Substituting the given values, we get:

N(400) = 900*(1/2)^(400/1600)
N(400) = 900*(1/2)^0.25
N(400) = 900*(0.8409)
N(400) = 757.8

Rounding to the nearest gram, we get:

Q = 757 grams

Therefore, the best choice is C.

The Half-Life of Radium Is Approximately 1,600 Years