Answer:
A. 2.25×10¹⁰ years
B. 9×10⁹ years
C. 15 g
D. 8.78 g
Step-by-step explanation:
From the question given above, the following data were obtained:
Half-life (t₁/₂) = 4.5×10⁹ years
A. Determination of how many years has gone by.
Half-life (t₁/₂) = 4.5×10⁹ years
Number of half-lives (n) = 5
Time (t) =?
t = n × t₁/₂
t = 5 × 4.5×10⁹
t = 2.25×10¹⁰ years
Therefore, 2.25×10¹⁰ years has gone by.
B. Determination of how many years has gone by.
We'll begin by calculating the number of half-lives that has elapse. This can be obtained as follow:
Original amount (N₀) = 240 g
Amount remaining (N) = 60 g
Number of half-lives (n) =?
N = 1/2ⁿ × N₀
60 = 1/2ⁿ × 240
Cross multiply
60 × 2ⁿ = 240
Divide both side 60
2ⁿ = 240/60
2ⁿ = 4
Express 4 in index form with 2 as the base
2ⁿ = 2²
n = 2
Finally, we shall determine how many years has gone by. This can be obtained as follow:
Half-life (t₁/₂) = 4.5×10⁹ years
Number of half-lives (n) =
Time (t) =?
t = n × t₁/₂
t = 2 × 4.5×10⁹
t = 9×10⁹years
Therefore, 9×10⁹ years has gone by.
C. Determination of the amount remaining.
We'll begin by calculating the number of half-lives that has elapse. This can be obtained as follow:
Half-life (t₁/₂) = 4.5×10⁹ years
Time (t) = 1.8×10¹⁰ years
Number of half-lives (n) = ?
t = n × t₁/₂
1.8×10¹⁰ = n × 4.5×10⁹
Divide both side by 4.5×10⁹
n = 1.8×10¹⁰ / 4.5×10⁹
n = 4
Finally, we shall determine the amount remaining. This can be obtained as follow:
Original amount (N₀) = 240 g
Number of half-lives (n) = 4
Amount remaining (N) =?
N = 1/2ⁿ × N₀
N = 1/2⁴ × 240
N = 1/16 × 240
N = 240 / 16
N = 15 g
Therefore, 15 g is remaining.
D. Determination of the amount remaining.
Original amount (N₀) = 562 g
Number of half-lives (n) = 6
Amount remaining (N) =?
N = 1/2ⁿ × N₀
N = 1/2⁶ × 562
N = 1/64 × 562
N = 562 / 64
N = 8.78 g
Therefore, 8.78 g is remaining.