In a nuclear explosion, 180 MeV energy was released per fission and a total energy of `8 xx 10^(13)` joules was released. Calculate the mass of uranium used in the explosion.

Answer

To solve the problem of calculating the mass of uranium used in a nuclear explosion, we will follow these steps:

### Step 1: Convert the energy released per fission from MeV to Joules
The energy released per fission is given as 180 MeV. We need to convert this to Joules using the conversion factor \(1 \text{ MeV} = 1.6 \times 10^{-13} \text{ Joules}\).

\[ \text{Energy per fission} = 180 \text{ MeV} \times 1.6 \times 10^{-13} \text{ Joules/MeV} = 2.88 \times 10^{-11} \text{ Joules} \]

### Step 2: Calculate the total number of fissions
We know the total energy released in the explosion is \(8 \times 10^{13} \text{ Joules}\). To find the total number of fissions (or uranium atoms that underwent fission), we divide the total energy by the energy released per fission.

\[ \text{Number of fissions} = \frac{\text{Total Energy}}{\text{Energy per fission}} = \frac{8 \times 10^{13} \text{ Joules}}{2.88 \times 10^{-11} \text{ Joules}} \approx 2.78 \times 10^{24} \text{ fissions} \]

### Step 3: Convert the number of fissions to moles
To find the number of moles of uranium, we use Avogadro's number, which is approximately \(6.022 \times 10^{23} \text{ atoms/mole}\).

\[ \text{Number of moles} = \frac{\text{Number of fissions}}{N_A} = \frac{2.78 \times 10^{24}}{6.022 \times 10^{23}} \approx 4.62 \text{ moles} \]

### Step 4: Calculate the mass of uranium
The molar mass of uranium is approximately \(238 \text{ g/mol}\). To find the total mass of uranium used, we multiply the number of moles by the molar mass.

\[ \text{Mass of uranium} = \text{Number of moles} \times \text{Molar mass} = 4.62 \text{ moles} \times 238 \text{ g/mol} \approx 1099.56 \text{ grams} \]

### Final Answer
The mass of uranium used in the explosion is approximately **1099.56 grams**.

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