Chemistry High School

5. how much of an 800-gram sample of potassium-40 will remain after 3.9 × 109 years of radioactive decay?
1) 50 grams
2)100 grams
3)200 grams
4)400 grams

Answers

Answer 1

The answer to how much of an 800-gram sample of potassium-40 will remain after 3.9 × 109 years of radioactive decay is option (3) "200 grams."

The amount of an 800-gram sample of potassium-40 that will remain after 3.9 × 109 years of radioactive decay can be calculated by using the radioactive decay law. The radioactive decay law states that the number of radioactive nuclei N of a sample decreases as a function of time t. This can be given by the equation N = N₀ e^(-λt)

Where N₀ is the initial number of radioactive nuclei, λ is the decay constant, and t is the time.

The decay constant is related to the half-life T½ of the radioactive isotope by the equation

T½ = ln2 / λ Given that the half-life of potassium-40 is 1.28 × 10^9 years,

we can find the decay constant as follows

λ = ln2 / T½

= ln2 / (1.28 × 10^9)

= 5.43 × 10^-10 year^-1

Substituting the given values into the radioactive decay law, we get

N = 800 e^(-5.43 × 10^-10 × 3.9 × 10^9)N ≈ 200 grams

Therefore, the answer is option (3) 200 grams.

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Related Questions

which of the following statements about miscible liquids is correct? i. the components form a homogeneous solution. ii. the partial pressure of each component is the vapor pressure of the mixture times the components mole fraction. iii. each component has its own vapor pressure.

Answers

Option i. the components form a homogeneous solution is correct statements about miscible liquids.

When we talk about miscible liquids, these are liquids that can mix in any proportion without separating, given that the components form a homogeneous solution.

The following statement about miscible liquids is correct: i. the components form a homogeneous solution.

Let's look at each option one by one:i. The components form a homogeneous solution.

Mixtures of liquids that are completely soluble in each other in all proportions are called miscible liquids.

For example, ethanol and water are miscible in each other.

The mixture of the two will be a homogeneous solution where the two components are completely blended

.ii. The partial pressure of each component is the vapor pressure of the mixture times the components mole fraction.

This statement applies to the Raoult's law for ideal solutions, which holds only for solutions of non-electrolytes.

According to Raoult's law, for an ideal solution, the partial pressure of each component in the vapor phase is equal to the product of the vapor pressure of the pure component and its mole fraction in the solution.

iii. Each component has its own vapor pressure.

This is a statement about immiscible liquids rather than miscible liquids.

In immiscible liquids, the components are not soluble in each other, so each component has its own vapor pressure and forms separate layers when mixed.

In conclusion, the correct statement about miscible liquids is that the components form a homogeneous solution.

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according to the ideal gas law, what happens to the volume of a gas when the pressure doubles (all else held constant)? apex

Answers

Pressure and volume are proportional in direct variation, with the temperature and the number of gas molecules constant.

According to the Ideal Gas Law, what happens to the volume of a gas when the pressure doubles (all else held constant)

If the pressure of a gas is doubled (all other variables being constant), the volume of the gas will be halved. The formula for the Ideal Gas Law is PV = nRT,

where P = pressure, V = volume,

n = number of moles of gas,

R = the universal gas constant, and T = temperature.

The law states that the product of pressure and volume is proportional to the absolute temperature of the gas when all other variables are constant.

In a fixed container with a fixed number of molecules, doubling the pressure reduces the volume by half. The relationship between pressure and volume is a positive linear one. Pressure and volume are proportional in direct variation, with the temperature and the number of gas molecules constant.

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A Grignard reaction will fail in the presence of which species? A diethyl ether B alkenes C aromatic groups D water

Answers

A Grignard reaction will fail in the presence of D) water. Grignard reactions involve the reaction of a Grignard reagent, typically an alkyl or aryl magnesium halide, with a variety of electrophiles to form new carbon-carbon bonds.

These reactions are highly sensitive to the presence of water (H2O). Water can react with the Grignard reagent, hydrolyzing it and preventing it from participating in the desired reaction.When water is present, it can protonate the alkyl or aryl magnesium halide species to form an alkane or an alcohol, respectively. This side reaction reduces the concentration of the Grignard reagent and prevents it from reacting with the desired electrophile. Therefore, the presence of water inhibits the success of a Grignard reaction.The other options listed (diethyl ether, alkenes, aromatic groups) do not interfere significantly with Grignard reactions and are often used as solvents or reactants in these reactions.

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