Strontium-90 is radioactive and has a half life of 28.8 years. How much of a 2.90mg sample would be left after 137. years? Round your answer to 2 significant digits. Also, be sure your answer has a unit symbol.

0.11 mg

Explanation:

From the question given above, the following were obtained:

Half life (t½) = 28.8 years

Original amount ((N₀) = 2.90 mg

Time (t) = 137 years

Amount remaining (N) =?

Next, we shall determine the rate of disintegration (K). This can be obtained as follow:

Rate of decay (K) = 0.693/ half life (t½)

K = 0.693 / t½

Half life (t½) = 28.8 years

Rate of decay (K) =?

K = 0.693 / t½

K = 0.693 / 28.8

K = 0.0241 /year

Finally, we shall determine amount remaining after 137 years as follow:

Original amount ((N₀) = 2.90 mg

Time (t) = 137 years

Rate of decay (K) = 0.0241 /year

Amount remaining (N) =?

Log (N₀/N) = kt/2.3

Log (2.9/N) = 0.0241 × 137 / 2.3

Log (2.9/N) = 3.3017 / 2.3

Log (2.9/N) = 1.4355

Take the antilog of 1.4355

2.9/N = antilog (1.4355)

2.9/N = 27.26

Cross multiply

2.9 = N × 27.26

Divide both side by 27.26

N = 2.9/27.26

N = 0.11 mg

Therefore, the amount remaining after 137 years is 0.11 mg

b is the correct answer

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