Answer:
2.48 g
Explanation:
From the question given above, the following data were obtained:
Original amount (N₀) = 10 g
Time (t) = 1407.6 million years
Amount remaining (N) =?
Next, we shall determine the rate of decay (K) of uranium-235. This can be obtained as follow:
NOTE: Uranium-235 has a half life of 700 million years.
Decay constant (K) =?
Half life (t½) = 700 million years
K = 0.693/t½
K = 0.693/700
K = 9.9×10¯⁴ / year
Therefore, Uranium-235 decay at a rate of 9.9×10¯⁴ / year.
Finally, we shall determine the amount of Uranium-235 remaining after 1407.6 million years as follow:
Original amount (N₀) = 10 g
Time (t) = 1407.6 million years
Decay constant (K) = 9.9×10¯⁴ / year
Amount remaining (N) =?
Log (N₀/N) = kt /2.3
Log (10/N) = (9.9×10¯⁴ × 1407.6) /2.3
Log (10/N) = 0.60588
10/N = antilog (0.60588)
10/N = 4.04
Cross multiply
10 = 4.04 × N
Divide both side by 4.04
N = 10/4.04
N = 2.48 g
Therefore, 2.48 g of uranium-235 is remaining after 1407.6 million years.
If you have a 10 gram sample of uranium-235 there would still be uranium-235 after 1407.6 million years - 2.5 grams.
The half-life of U-235 is the time it takes for half the U to decay. We know that U-235 has 703.8 million years as its half-life which means it takes 703.8 million years to half of its initial amount.
We can construct a table as follows:
No. of Fraction Amount
half-lives t/(yr × 10⁶) remaining remaining/g
1 703.8 ½ 10/2 = 5
2 1407.6 ¼ 10/4 = 2.50
Thus, the correct answer is - 2.5 grams.
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