The table shows the amount of radioactive element remaining in a sample over a period of time. radioactive decay rateamount of radioactive sample(grams) 56.0 47.1 39.6 33.3 28 time(years)04008001,2001,600each correspond w eachotherpart 1: what is the half-life of the element? explain how you determined this. part 2: how long would it take 312 g of the sample to decay to 9.75 grams? show your work or explain your answer

8,000 years.

Explanation:

Part 1: What is the half-life of the element? Explain how you determined this.

Half-life time is the time needed for the reactants to be in its half concentration.

The sample stats with 56.0 g and reaches its half concentration (28.0 g) after 1,600 years.

So, the half-life of the sample is 1,600 years.

Part 2: How long would it take 312 g of the sample to decay to 9.75 grams? Show your work or explain your answer.

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 years.

number of molecules / avogadro's number * molecule molecular = mass

explanation:

we define a gram-molecular weight as the mass of one mole of any element or compound. a mole contains avogadro's number of units (molecules) –  

6.022

x

10

23

. so, dividing the number of molecules by avogadro's number gives us the number of moles. multiplying that by the molecular weight gives us the mass. from the periodic table we find the gram-molecular weight of u to be238 and of f to be19. so,  

u

f

6

will have a gram-molecular weight of 352g.

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