Answer:
1. The half-life is 22 years.
2. 132 years
Explanation:
1. Determination of the the half-life.
The half-life of an element is the time taken for half the element to decay.
From the table given above, the original amount of the element 45 g. If we divide 45 by 2, we'll have 22.5 g as half the original amount of element.
Now, the time taken to obtain 22.5 g as shown from the table is 22 years.
Thus, the half-life the element is 22 years.
2. Determination of the time.
Original amount (N₀) = 308 g
Amount remaining (N) = 4.8125 g
Time (t) =?
Next, we shall the number of half-lives that has elapsed. This can be obtained as follow:
Original amount (N₀) = 308 g
Amount remaining (N) = 4.8125 g
Number of half-lives (n) =?
N = 1/2ⁿ × N₀
4.8125 = 1/2ⁿ × 308
Cross multiply
4.8125 × 2ⁿ = 308
Divide both side by 4.8125
2ⁿ = 308 / 4.8125
2ⁿ = 64
Express 64 in index form with 2 as the base.
2ⁿ = 2⁶
n = 6
Thus, 6 half-lives has elapsed.
Finally, we shall determine the time. This can be obtained as follow:
Number of half-lives (n) = 6
Half-life (t½) = 22 years
Time (t) =?
n = t / t½
6= t / 22 years
Cross multiply
t = 6 ×22
t = 132 years.
Thus, the time taken is 132 years.
