Calculate the amount of`""_(92)U^(235)` required to release energy of 1 kWh. Given energy released during fission of one atom is 200 MeV.

Answer

To calculate the amount of Uranium-235 required to release energy of 1 kWh, we will follow these steps:

### Step 1: Convert 1 kWh to Joules
1 kWh = 1000 Wh
1 hour = 3600 seconds
Therefore,
1 kWh = 1000 W × 3600 s = 3.6 × 10^6 Joules

### Step 2: Convert the energy released per fission from MeV to Joules
The energy released during the fission of one Uranium-235 atom is given as 200 MeV.
To convert MeV to Joules, we use the conversion factor:
1 eV = 1.6 × 10^(-19) Joules
Thus,
200 MeV = 200 × 10^6 eV = 200 × 10^6 × 1.6 × 10^(-19) Joules
Calculating this gives:
Energy per fission = 200 × 1.6 × 10^(-13) Joules = 3.2 × 10^(-11) Joules

### Step 3: Calculate the number of fissions required to release 1 kWh
To find the number of fissions (N) required to release 3.6 × 10^6 Joules, we use the formula:
N = Total energy required / Energy released per fission
N = (3.6 × 10^6 Joules) / (3.2 × 10^(-11) Joules)
Calculating this gives:
N = 1.125 × 10^17 fissions

### Step 4: Calculate the number of moles of Uranium-235 atoms
Using Avogadro's number (N_A = 6.023 × 10^23 atoms/mole), we can find the number of moles (n) of Uranium-235 required:
n = N / N_A
n = (1.125 × 10^17) / (6.023 × 10^23)
Calculating this gives:
n ≈ 1.87 × 10^(-6) moles

### Step 5: Calculate the mass of Uranium-235 required
The molar mass of Uranium-235 is approximately 235 grams/mole.
Mass = n × Molar mass
Mass = (1.87 × 10^(-6) moles) × (235 g/mole)
Calculating this gives:
Mass ≈ 0.000439 grams or 0.439 mg

### Final Answer
The amount of Uranium-235 required to release energy of 1 kWh is approximately **0.439 mg**.

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