Energy released during the fission of one Uranium-235 nucleus is 200MeV. Energy released by the fission of 500gm of U-235 nuclei will be about

Options

A. `3.5xx10^20` MeV
B. `6.6xx10^24` MeV
C. `2.8xx10^26` MeV
D. `1.6xx10^31` MeV

Answer

To solve the problem of calculating the energy released by the fission of 500 grams of Uranium-235 (U-235), we can follow these steps:

### Step 1: Calculate the number of moles of U-235 in 500 grams.
The molar mass of U-235 is approximately 235 g/mol.

\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{500 \text{ g}}{235 \text{ g/mol}} \approx 2.13 \text{ moles} \]

### Step 2: Calculate the number of U-235 nuclei in 2.13 moles.
Using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) nuclei/mole, we can find the total number of nuclei.

\[ \text{Number of nuclei} = \text{Number of moles} \times \text{Avogadro's number} = 2.13 \text{ moles} \times 6.022 \times 10^{23} \text{ nuclei/mole} \approx 1.28 \times 10^{24} \text{ nuclei} \]

### Step 3: Calculate the total energy released by the fission of these nuclei.
Given that the energy released by the fission of one U-235 nucleus is 200 MeV, we can find the total energy released by multiplying the number of nuclei by the energy per nucleus.

\[ \text{Total energy} = \text{Number of nuclei} \times \text{Energy per nucleus} = 1.28 \times 10^{24} \text{ nuclei} \times 200 \text{ MeV} \]

\[ \text{Total energy} = 2.56 \times 10^{26} \text{ MeV} \]

### Final Answer:
The energy released by the fission of 500 grams of U-235 nuclei will be about \(2.56 \times 10^{26} \text{ MeV}\).

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