Answer:
25 g
Step-by-step explanation:
The following data were obtained from the question:
Half life (t½) = 5 s
Original amount (N₀) = 100 g
Time (t) = 10 s
Amount remaining (N) =..?
Next, we shall determine the decay constant for the disintegration. This can be obtained as follow:
Half life (t½) = 5 s
Decay constant (K) =.?
K = 0.693 / t½
K = 0.693 / 5
K = 0.1386 s¯¹
Finally, we shall determine the amount of the isotope that remained after 10 s as follow:
Original amount (N₀) = 100 g
Time (t) = 10 s
Decay (K) = 0.1386 s¯¹
Amount remaining (N) =..?
Log (N₀/N) = kt /2.303
Log (100/N) = (0.1386 × 10) / 2.303
Log (100/N) = 1.386 / 2.303
Log (100/N) = 0.6018
Take the anti log of 0.6018
100/N = antilog (0.6018)
100/N = 4
Cross multiply
100 = N × 4
Divide both side by 4
N = 100/4
N = 25 g
Therefore, the amount remaining after 10 s is 25 g