To solve the problem of calculating the amount of energy released by the fission of 0.235 g of Uranium-235 (U-235), we can follow these steps:
### Step 1: Calculate the number of nuclei in 0.235 g of U-235
To find the number of nuclei, we need to use the formula:
\[
\text{Number of nuclei} = \frac{\text{mass of U-235}}{\text{molar mass of U-235}} \times N_A
\]
Where:
- Mass of U-235 = 0.235 g
- Molar mass of U-235 = 235 g/mol
- \(N_A\) (Avogadro's number) = \(6.022 \times 10^{23}\) nuclei/mol
Substituting the values:
\[
\text{Number of nuclei} = \frac{0.235 \, \text{g}}{235 \, \text{g/mol}} \times 6.022 \times 10^{23} \, \text{nuclei/mol}
\]
Calculating this gives:
\[
\text{Number of nuclei} = \frac{0.235}{235} \times 6.022 \times 10^{23} = 6.022 \times 10^{20} \, \text{nuclei}
\]
### Step 2: Calculate the total energy released
Given that the energy released per fission of one U-235 nucleus is 180 MeV, we can calculate the total energy released by multiplying the number of nuclei by the energy per fission:
\[
\text{Total energy} = \text{Number of nuclei} \times \text{Energy per fission}
\]
Substituting the values:
\[
\text{Total energy} = 6.022 \times 10^{20} \, \text{nuclei} \times 180 \, \text{MeV}
\]
Calculating this gives:
\[
\text{Total energy} = 1.084 \times 10^{23} \, \text{MeV}
\]
### Step 3: Convert MeV to joules
To convert MeV to joules, we use the conversion factor:
\[
1 \, \text{MeV} = 1.602 \times 10^{-13} \, \text{J}
\]
Thus, we convert the total energy:
\[
\text{Total energy in joules} = 1.084 \times 10^{23} \, \text{MeV} \times 1.602 \times 10^{-13} \, \text{J/MeV}
\]
Calculating this gives:
\[
\text{Total energy in joules} \approx 1.736 \times 10^{10} \, \text{J}
\]
### Step 4: Convert joules to kilojoules
To convert joules to kilojoules, we divide by 1000:
\[
\text{Total energy in kilojoules} = \frac{1.736 \times 10^{10} \, \text{J}}{1000} = 1.736 \times 10^{7} \, \text{kJ}
\]
### Final Answer
The total energy released by the fission of 0.235 g of U-235 is approximately \(1.736 \times 10^{7} \, \text{kJ}\).
---
