Physics 2005 JAMB Past Questions - Question 12: The amount of energy released when 0.5 kg of uranium is burnt completely is

Correct Answer

A

Explanation

E=mc2=0.5(3*108)=4.5*1016JWhen uranium is "burned" or undergoes nuclear fission, it releases a significant amount of energy. The amount of energy released from the complete combustion of a specific mass of uranium depends on its isotopic composition, but for the sake of a rough estimate, we can consider uranium-235 (U-235) since it's one of the most commonly used isotopes for nuclear energy production.

The energy released per fission of U-235 is approximately 200 MeV (mega-electron volts). To calculate the energy released when 0.5 kg of U-235 undergoes complete fission, you'll need to convert the mass to the number of uranium atoms and then multiply it by the energy per fission.

First, calculate the number of moles of U-235 in 0.5 kg:

1. Find the molar mass of U-235. The molar mass of U-235 is approximately 235 g/mol.

2. Convert the mass from kilograms to grams: 0.5 kg = 500 grams.

3. Calculate the number of moles:
 
  moles = mass (in grams) / molar mass
  moles = 500 g / 235 g/mol ≈ 2.13 moles

Now that you have the number of moles of U-235, you can calculate the total energy released by fissioning all these moles.

1 mole of U-235 contains approximately 6.022 x 10^23 U-235 atoms.

So, the number of U-235 atoms in 2.13 moles is:

2.13 moles x 6.022 x 10^23 atoms/mole ≈ 1.28 x 10^24 U-235 atoms

Each U-235 atom releases 200 MeV per fission. To convert MeV to joules, you can use the conversion factor:

1 MeV = 1.60218 x 10^-13 joules

Now, calculate the total energy released:

Total energy = (Number of U-235 atoms) x (Energy per fission)
Total energy ≈ (1.28 x 10^24 atoms) x (200 MeV) x (1.60218 x 10^-13 J/MeV) ≈ 4.09 x 10^11 joules

So, when 0.5 kg of uranium-235 is burned completely, it releases approximately 4.09 x 10^11 joules of energy.