The table shows the amount of radioactive element remaining in a sample over a period of time. Part 1: what is the half life of the element? Explain how you determined this. Part 2: how long would it take 308 g of the sample to decay to 4.8125 grams? Show your work or explain your answer? * please explain the answer is easy to understand terms, thank you*

pt1

The half-life of the element is 1,600 years.

pt2

k = ln(2)/(t1/2) = 0.693/(t1/2).

Where, k is the rate constant of the reaction.

t1/2 is the half-life of the reaction.

∴ k =0.693/(t1/2) = 0.693/(1,600 years) = 4.33 x 10⁻⁴ year⁻¹.

kt = ln([A₀]/[A]),

where, k is the rate constant of the reaction (k = 4.33 x 10⁻⁴ year⁻¹).

t is the time of the reaction (t = ??? year).

[A₀] is the initial concentration of the sample ([A₀] = 312.0 g).

[A] is the remaining concentration of the sample ([A] = 9.75 g).

∴ t = (1/k) ln([A₀]/[A]) = (1/4.33 x 10⁻⁴ year⁻¹) ln(312.0 g/9.75 g) = [8,000 year].

-Hops

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