Question

A sample of Bismuth-212 has a mass of 2.64 grams (g) after 121 seconds (s). What was the initial mass of the sample if Bismuth-212 has a half-life of 60.5 s?
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1 point

Answer 1

To solve this problem, we can use the equation for exponential decay:

m(t) = m0 * (1/2)^(t/t1/2)

Where:
m(t) = final mass after time t
m0 = initial mass
t = time elapsed
t1/2 = half-life of the substance

Given that:
m(t) = 2.64 g
t = 121 s
t1/2 = 60.5 s

Plugging in the values:

2.64 = m0 * (1/2)^(121/60.5)

2.64 = m0 * (1/2)^2 = m0 * (1/4)

Now, we can solve for m0:

m0 = 2.64 * 4 = 10.56 g

Therefore, the initial mass of the Bismuth-212 sample was 10.56 grams.