Answer:
3.99 g
Explanation:
The following data were obtained from the question:
Half life (t½) = 2 years.
Original amount (N₀) = 128 g
Time (t) = 10 years
Amount remaining (N) =..?
Next, we shall determine the rate of disintegration of the isotope. This can be obtained as follow:
Half life (t½) = 2 years.
Decay constant (K) =.?
K= 0.693/t½
K = 0.693/2
K = 0.3465 year¯¹.
Finally, we shall determine the amount remaining after 10 years i.e the amount remaining when they arrive on Earth. This can be obtained as follow:
Original amount (N₀) = 128 g
Time (t) = 10 years
Decay constant (K) = 0.3465 year¯¹.
Amount remaining (N) =..?
Log (N₀/N) = kt/2.3
Log (128/N) = (0.3465 × 10)/2.3
Log (128/N) = 1.5065
Take the antilog of 1.5065
128/N = Antilog (1.5065)
128/N = 32.1
Cross multiply
128 = 32.1 × N
Divide both side by 32.1
N = 128/32.1
N = 3.99 g
Therefore, the amount remaining is 3.99 g
