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------------------------------------------------ In a particular fission of a uranium-235 ([tex]^{235}U[/tex]) nucleus, which has a neutral atomic mass of 235.0439 u, a reaction energy of 200 MeV is released.

(a) A mass of 1.00 kg of pure uranium-235 contains how many atoms?

(b) How much total energy is released if the entire mass of 1.00 kg of uranium-235 fissions?

(c) Suppose that these fission reactions occur at a rate to release a constant 100 W of power to a lamp for a long period of time. Assuming 100% of the reaction energy goes into powering the lamp, for how many years can the lamp run?

A particular fission of a uranium-235 (235 U) nucleus, which has neutral atomic mass 235.0439 u, a reaction energy of 200 MeV is released.(a)1.00 kg of pure uranium contains approximately 2.56 x 10^24 uranium-235 atoms.(b)the total energy released if the entire mass of 1.00 kg of uranium-235 undergoes fission is approximately 3.11 x 10^13 joules.(c)assuming 100% of the reaction energy goes into powering the lamp, the lamp can run for approximately 983,544 years.

(a) To determine the number of uranium-235 (235U) atoms in 1.00 kg of pure uranium, we need to use Avogadro's number and the molar mass of uranium-235.

Calculate the molar mass of uranium-235 (235U):

Molar mass of uranium-235 = 235.0439 g/mol

Convert the mass of uranium to grams:

Mass of uranium = 1.00 kg = 1000 g

Calculate the number of moles of uranium-235:

Number of moles = (Mass of uranium) / (Molar mass of uranium-235)

Number of moles = 1000 g / 235.0439 g/mol

Use Avogadro's number to determine the number of atoms:

Number of atoms = (Number of moles) × (Avogadro's number)

Now we can perform the calculations:

Number of atoms = (1000 g / 235.0439 g/mol) × (6.022 x 10^23 atoms/mol)

Number of atoms ≈ 2.56 x 10^24 atoms

Therefore, 1.00 kg of pure uranium contains approximately 2.56 x 10^24 uranium-235 atoms.

(b) To calculate the total energy released if the entire mass of 1.00 kg of uranium-235 undergoes fission, we need to use the energy released per fission and the number of atoms present.

Given:

Reaction energy per fission = 200 MeV (mega-electron volts)

Convert the reaction energy to joules:

1 MeV = 1.6 x 10^-13 J

Energy released per fission = 200 MeV ×(1.6 x 10^-13 J/MeV)

Calculate the total number of fissions:

Total number of fissions = (Number of atoms) × (mass of uranium / molar mass of uranium-235)

Multiply the energy released per fission by the total number of fissions:

Total energy released = (Energy released per fission) × (Total number of fissions)

Now we can calculate the total energy released:

Total energy released = (200 MeV) * (1.6 x 10^-13 J/MeV) × [(2.56 x 10^24 atoms) × (1.00 kg / 235.0439 g/mol)]

Total energy released ≈ 3.11 x 10^13 J

Therefore, the total energy released if the entire mass of 1.00 kg of uranium-235 undergoes fission is approximately 3.11 x 10^13 joules.

(c) To calculate the number of years the lamp can run, we need to consider the power generated by the fission reactions and the total energy released.

Given:

Power generated = 100 W

Total energy released = 3.11 x 10^13 J

Calculate the time required to release the total energy at the given power:

Time = Total energy released / Power generated

Convert the time to years:

Time in years = Time / (365 days/year ×24 hours/day ×3600 seconds/hour)

Now we can calculate the number of years the lamp can run:

Time in years = (3.11 x 10^13 J) / (100 W) / (365 days/year × 24 hours/day * 3600 seconds/hour)

Time in years ≈ 983,544 years

Therefore, assuming 100% of the reaction energy goes into powering the lamp, the lamp can run for approximately 983,544 years.

To learn more about Avogadro's number visit: https://brainly.com/question/859564

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