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

Answer 1

A) Correct answer is : 5.27 mg

B) Correct answer is : 0 mg

C) Correct answer is : 1.02 x 10^-1 mg

Explanation

A) initial amount of Rn = 5.37 mg

time passed = 2.5 hours

half-life = 3.82 days

half-life = 3.82 days * (24 hr/day)

half-life = 91.68 hours

half-lives passed = (time passed) / (half-life)

half-lives passed = (2.5 hours) / (91.68 hours)

half-lives passed = 0.027

According to the radioactive decay law,

final amount = (initial amount) / (2^a)

where 'a' is the half-lives passed

final amount = (5.37 mg) / (2^0.027)

final amount = (5.37 mg) / (1.019)

final amount = 5.27 mg