If you have 24 grams of an unstable atom with a half life of 5,000 years, how many grams would be left after 15,000 years

3 g.

Explanation:

The following data were obtained from the question:

Original amount (N₀) = 24 g

Half life (t½) = 5000 years

Time (t) = 15000 years

Amount remaining (N) =?

Next, we shall determine the rate constant K. This can be obtained as follow:

Half life (t½) = 5000 years

Rate constant (K) =.?

K = 0.693 / t½

K = 0.693 / 5000

K = 1.386×10¯⁴ / years

Finally, we shall determine the amount remaining (N) after 15000 years as follow:

Original amount (N₀) = 24 g

Time (t) = 15000 years

Rate constant (K) = 1.386×10¯⁴ / years

Amount remaining (N) =?

Log (N₀/N) = kt/2.3

Log (24/N) = 1.386×10¯⁴ × 15000/2.3

Log (24/N) = 2.079/2.3

Log (24/N) = 0.9039

24/N = antilog (0.9039)

24/N = 8.01

Cross multiply

24 = N × 8.01

Divide both side by 8.01

N = 24/8.01

N = 3 g

Therefore, the amount remaining after 15000 years is 3 g.

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d.) gravity pulled particles of dust and gas together to form planets.