Radon-222 is a radioactive gas with a half-life of 3.82 days. How long would it take for seven-eighths of a sample of radon-222 to decay?

Answer 1

The formula for a half life calculation (in it's simplified form) is the following

X = X₀(1/2)^{t/(half life)}

As 7/8th's of the radon has decayed, 1/8 remains, indicating that the time passed results in (1/2)³ remaining radon. In other words, three half lives have passed. Knowing the half life is 3.82 days, 3 x 3.82 = 11.46 days would result in 3 half lives and 1/8 of the radon remaining.

Therefore the answer would be 11.46 days