Potassium-40 can decay into either calcium-40 or argon-40. all three of these atoms have essentially the same weight. ninety percent of the potassium-40 will decay into calcium-40, and only ten percent will decay into argon-40. when argon-40 is produced by the radioactive decay of potassium-40 inside a rock, the argon-40 produced by the decay is a gas and is trapped inside the rock. the amount argon-40 trapped in a rock can be measured by grinding up the rock and capturing the liberated argon-40 gas. suppose the amount of potassium-40 inside a rock is measured to be 0.81 milligrams, and the amount of argon-40 gas trapped in the rock is measured to be 0.377 milligrams. 1. how much of the potassium-40 that was originally present inside the rock has undergone radioactive decay to produce argon-40?

Answser:

3.77 mg of K-40 decayed into Ar-40.

Data:

1) K-40, Ca-40, Ar-40: all three have the same atomic mass
2) 90% of the potassium-40 will decay into calcium-40
3) 10% of the potassium-40 will decay into argon-40.
4) K-40 inside the rock = 0.81 mg
5) Ar-40 trapped = 0.377 mg

Soltuion:

1) 0.377 mg of Ar-40 is the 10% of the mass of the K-40 that decayed

=> x * 10% = 0.377 mg => x * 0.1 = 0.377mg

=> x = 0.377 mg / 0.1 = 3.77 mg

That means that 3.77 mg of K-40 decayed into Ar-40. And this is the answer to the question.

Additionaly, you can analyze the content of all K-40 and Ca-40, to understand better the case.

2) The mass of the K-40 that decayed into Ca-40 is 9 times (ratio 9:1) the amount that decayed into Ar-40 =>

mass of K-40 that decayed into Ca-40 = 9 * 0.377 = 3.393 mg

3) Total amount of K-40 that decayed = amount that decayed into Ar-40 + amount that decayed into Ca-40 = 0.377mg + 3.393mg = 3.77 mg

4) Original amount of K-40 = amount of K-40 that decayed + amount of K-40 present in the rock = 3.77mg + 0.81 mg = 4.58 mg

5) amount of K-40 that decayed into Ar-40 as percent

% = [3.77 mg / 4.58mg] * 100 = 82.31 %.

Answer:

a. energy is absorbed in the reaction.

explanation:

if in a given reaction the energy of products is greater than the energy of reactants it means that reaction is endothermic and during the reaction, the energy is absorbed by reactants. in an endothermic reaction, the products have more stored chemical energy than the reactants. and in this reaction the reactants are more stable than products before the compounds with less energy are always more stable.