How much energy will be released when 10 kg of `U^(235)` is completely converts into energy :

Options

A. `5 xx 10^(27) Me V`
B. ` 5 xx 10^(24) Me V`
C. ` 9 xx 10^(17) J`
D. All of these

Answer

To find out how much energy will be released when 10 kg of Uranium-235 (U-235) is completely converted into energy, we can use Einstein's mass-energy equivalence principle, which is given by the equation:

\[ E = mc^2 \]

Where:
- \( E \) is the energy released,
- \( m \) is the mass converted into energy,
- \( c \) is the speed of light in vacuum (\( c \approx 3 \times 10^8 \, \text{m/s} \)).

### Step 1: Convert mass from kg to grams
Since we often deal with atomic mass in grams, we first convert 10 kg of U-235 into grams.

\[ 10 \, \text{kg} = 10,000 \, \text{g} \]

### Step 2: Calculate the number of moles of U-235
The molar mass of U-235 is approximately 235 g/mol. We can find the number of moles of U-235 in 10,000 g.

\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{10,000 \, \text{g}}{235 \, \text{g/mol}} \approx 42.55 \, \text{moles} \]

### Step 3: Calculate the number of atoms in U-235
Using Avogadro's number (\( N_A \approx 6.022 \times 10^{23} \, \text{atoms/mol} \)), we can calculate the total number of atoms in the U-235.

\[ \text{Number of atoms} = \text{Number of moles} \times N_A \]
\[ \text{Number of atoms} \approx 42.55 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 2.56 \times 10^{25} \, \text{atoms} \]

### Step 4: Calculate the energy released per atom
According to the information provided, when one atom of U-235 is converted into energy, it releases approximately 200 MeV (million electron volts).

To convert MeV to joules, we use the conversion factor:
\[ 1 \, \text{MeV} = 1.6 \times 10^{-13} \, \text{J} \]

Thus, the energy released per atom in joules is:
\[ E_{\text{per atom}} = 200 \, \text{MeV} \times 1.6 \times 10^{-13} \, \text{J/MeV} \approx 3.2 \times 10^{-11} \, \text{J} \]

### Step 5: Calculate the total energy released
Now, we can find the total energy released when all atoms of U-235 are converted into energy.

\[ E_{\text{total}} = \text{Number of atoms} \times E_{\text{per atom}} \]
\[ E_{\text{total}} \approx 2.56 \times 10^{25} \, \text{atoms} \times 3.2 \times 10^{-11} \, \text{J} \approx 8.19 \times 10^{14} \, \text{J} \]

### Final Answer
The total energy released when 10 kg of U-235 is completely converted into energy is approximately:

\[ E_{\text{total}} \approx 8.19 \times 10^{14} \, \text{J} \]

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