If we start with 1.000 g of strontium-90,0.908 g will remain after 4.00 y.This means that the half-life Of strontium-90 is ________ y.

Question

Quizplus · Accepted Answer

The half-life of a radioactive substance is the time it takes for half of the initial amount to decay. Using the formula for exponential decay:

N = N0 * (1/2)^(t/T)

where N is the final amount, N0 is the initial amount, t is time, and T is the half-life, we can solve for T:

0.908 g = 1.000 g * (1/2)^(4/T)

Taking the natural logarithm of both sides:

ln(0.908) = ln(1.000) + ln(1/2)^(4/T) = ln(1/2)^(4/T)

ln(0.908) = -0.0927

ln(1/2)^(4/T) = -0.0927

(4/T) * ln(1/2) = -0.0927

T = -4 / ln(1/2) * 0.0927

T = 28.7 years (rounded to one decimal place)

Therefore, the half-life of strontium-90 is 28.7 years, and the best choice is C.

If We Start with 1