The alpha decay of Radon-222 into Polonium-218 is followed by the alpha decay of
ID: 545673 • Letter: T
Question
The alpha decay of Radon-222 into Polonium-218 is followed by the alpha decay of Polonium-218 into Lead-214 as shown below:
22286Rn --> 21884Po + 42He --> 21482Pb + 42He
The half-lives of Radon-222 and Polonium-218 are 3.82 days and 3.05 minutes respectively.
A) If a 5.37 mg sample of radon is initially pure, how much remains after 2.5 hours? Answer choices: 5.37 mg, 5.27 mg, 3.51 mg, or 0 mg
B) How many mg of polonium will be produced in 2.5 hours? Answer choices: 3.51 mg, 0.0117 mg, 2.93 x 10-3 mg, or 0 mg
C) How many mg of lead will be produced in 2.5 hours? Answer choices: 2.93 x 10-3 mg, 1.80 x 10-2 mg, 1.02 x 10-1 mg, or 5.35 mg
Explanation / Answer
A)
Half life-time(T1/2) = 3.82 days = (3.82*24) = 91.68 hr
K1 = 0.693/T1/2
= 0.693/91.68
= 0.00756 hr-1
initial concentration(a) = 5.37 mg
after 2.5 hr concentration(a-x) = ?
K1 = (1/t)ln(a/a-x)
t = time = 2.5 hr
K1 = 0.00756 hr-1
0.00756 = (1/2.5)ln(5.37/y)
a-x = y = 5.2695 mg
answer: 5.27 mg
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