A 1.00 g sample of $ { }_{32}^{66} \mathrm{Ge} $ decays to 0.87 g in 1.9 hr.What is the half-life of $ { }_{32}^{66} \mathrm{Ge} $?

Question

Quizplus · Accepted Answer

- First, we need to calculate how much of the sample has decayed using the following formula:

Amount of substance left = Initial amount of substance x (1/2)^(t/half-life)

Where t is the time elapsed and half-life is the time taken for half of the sample to decay.

- Let's plug in the given values:

0.87 g = 1.00 g x (1/2)^(1.9/half-life)

- Now, we can solve for the half-life:

(1/2)^(1.9/half-life) = 0.87/1.00

(1/2)^(1.9/half-life) = 0.87

Take the natural logarithm of both sides:

ln(1/2)^(1.9/half-life) = ln(0.87)

(1.9/half-life)ln(1/2) = ln(0.87)

(1.9/half-life) = ln(0.87)/ln(1/2)

half-life = 4.5 hr

Therefore, the correct answer is C.

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