HELP PLEASE, I NEED THIS BY TODAY! If you have a 10 gram sample of uranium-235 how much would still be uranium-235 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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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.

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