Answer:
15.32 days
Explanation:
From the question given above, the following data were obtained:
Half-life (t½) = 3.83 days
Original amount (N₀) = 225 g
Amount remaining (N) = 14.06 g
Time (t) =.?
Next, we shall determine the number of half-lives that has elapsed. This can be obtained as follow:
Original amount (N₀) = 225 g
Amount remaining (N) = 14.06 g
Number of half-lives (n) =?
N = N₀ / 2ⁿ
14.06 = 225 / 2ⁿ
Cross multiply
14.06 × 2ⁿ = 225
Divide both side by 14.06
2ⁿ = 225 / 14.06
2ⁿ = 16
Express 16 in index form with 2 as the base
2ⁿ = 2⁴
n = 4
Thus, 4 half-lives has elapsed.
Finally, we shall determine the time. This can be obtained as follow:
Half-life (t½) = 3.83 days
Number of half-lives (n) = 4
Time (t) =.?
n = t / t½
4 = t / 3.83
Cross multiply
t = 4 × 3.83
t = 15.32 days
Therefore the time for 225 g sample of Radon to decay to 14.06 g is 15.32 days
