Answer:
30.2 years
Step-by-step explanation:
From the question given above, the following data were obtained:
Original amount (Nₒ) = 7.48E-3
Amount remaining (N) = 1.87E-3
Time (t) = 60.4 years
Half-life (t½) =?
Next, we shall determine the number of half-lives that has elapse. This can be obtained as follow:
Original amount (Nₒ) = 7.48E-3 = 7.48×10¯³
Amount remaining (N) = 1.87E-3 = 1.87×10¯³
Number of half-lives (n) =?
N = 1/2ⁿ × Nₒ
1.87×10¯³ = 1/2ⁿ × 7.48×10¯³
Cross multiply
1.87×10¯³ × 2ⁿ = 7.48×10¯³
Divide both side by 1.87×10¯³
2ⁿ = 7.48×10¯³ / 1.87×10¯³
2ⁿ = 4
Express 4 in index form with 2 as the base
2ⁿ = 2²
n = 2
Thus, 2 half-lives has elapsed.
Finally, we shall determine the half-life of the cesium-137. This can be obtained as follow:
Time (t) = 60.4 years
Number of half-lives (n) = 2
Half-life (t½) =?
n = t / t½
2 =60.4 / t½
Cross multiply
2 × t½ = 60.4
Divide both side by 2
t½ = 60.4 / 2
t½ = 30.2 years
Thus, the half-life of the cesium-137 is 30.2 years