Chemistry, 04.10.2019 23:00 natalieburnett82

The table shows the amount of radioactive element remaining in a sample over a period of time.

radioactive decay rate

amount of radioactive sample

(grams) time

(years)

56.0 0

47.1 400

39.6 800

33.3 1,200

28 1,600

part 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.

Answers: 1

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Answer from: xxhighwolfxx7508

8,000 year.

Explanation:

It is known that the decay of a radioactive isotope isotope obeys first order kinetics.Half-life time is the time needed for the reactants to be in its half concentration.If reactant has initial concentration [A₀], after half-life time its concentration will be ([A₀]/2).Also, it is clear that in first order decay the half-life time is independent of the initial concentration.

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

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

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.

For, first order reactions:

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.

Also, we have the integral law of first order reaction:

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.

Answer from: whiteshawn02

Half life of the sample= 1600 years

Part 2: 8000 years

Explanation:

The half life of a radioactive substance is the time taken for the substance to decay to half its initial amount.

Since 56.0g of radioactive material was present at t= 0 years. Half of 56.0g is 28.0g hence the time taken to have 28.0g of the sample left is the half life of the material.

If the original sample contained 312g of radioactive material

First half life. 156g left

Second half life. 78 g left

Third half life. 39gleft

Fourth half life. 19.5 g left

Fifth half life. 9.75 g

If each half life takes 1600 years then five half life will take 5×1600= 8000 years

Answer from: Quest

The answer to your question really depends on three things: how much water you have, how cold it is to start out, and how cold the things around it are. water actually freezes when it gets to 32 degrees fahrenheit (0 degrees celsius), but the time it takes to get there may be different. let's start with the first. if you take two glasses, and fill one with a tiny bit of water, and the other about halfway, then put them both in the freezer, the one with less water will freeze first (you can try this at home, but i recommend using plastic cups and not glass ones). now let's move on to the second part. let's say you have two glasses, and you fill one with really cold water that has been in the refrigerator, and the other with really hot water from the sink. if you put both of them in the freezer, the one that started out colder will freeze first. for the third part, let's imagine that you have two glasses with the same amount of water in them, and the water is at the same temperature. imagine putting one outside on a really really cold day in georgia, and having a friend in alaska put one outside on the same day. since it would be so much colder in alaska, the glass of water there would freeze before yours. so, if you took a tiny bit of really cold water in a glass, and put it outside on a cold day in alaska, it would freeze a lot faster than a big glass of hot water outside on a cold day in georgia.

Answer from: Quest

It will appear as o2(g) as a reactant

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The table shows the amount of radioactive element remaining in a sample over a period of time.
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