Calculate the energy released in the fissionn reaction
`""^(235)U+nto""^(141)Cs+""^(93)Rb+2n`
Here are some atomic and particle masses.
`""^(235)U" "235.04392u" """^(93)Rb" "92.92157u`
`""^(141)Cs" "140.91963u" "n" "1.00866u`

Answer

To calculate the energy released in the fission reaction \( ^{235}\text{U} + n \rightarrow ^{141}\text{Cs} + ^{93}\text{Rb} + 2n \), we will follow these steps:

### Step 1: Write down the mass of each particle involved in the reaction.
- Mass of \( ^{235}\text{U} = 235.04392 \, u \)
- Mass of neutron \( n = 1.00866 \, u \)
- Mass of \( ^{141}\text{Cs} = 140.91963 \, u \)
- Mass of \( ^{93}\text{Rb} = 92.92157 \, u \)

### Step 2: Calculate the total mass before the reaction.
The total mass before the reaction is the sum of the mass of uranium and the neutron:
\[ m_{\text{initial}} = m_{^{235}\text{U}} + m_n = 235.04392 \, u + 1.00866 \, u = 236.05258 \, u \]

### Step 3: Calculate the total mass after the reaction.
The total mass after the reaction includes the masses of the fission products and the neutrons produced:
\[ m_{\text{final}} = m_{^{141}\text{Cs}} + m_{^{93}\text{Rb}} + 2 \cdot m_n = 140.91963 \, u + 92.92157 \, u + 2 \cdot 1.00866 \, u \]
Calculating the mass of the neutrons:
\[ 2 \cdot m_n = 2 \cdot 1.00866 \, u = 2.01732 \, u \]
Now, summing up:
\[ m_{\text{final}} = 140.91963 \, u + 92.92157 \, u + 2.01732 \, u = 235.85852 \, u \]

### Step 4: Calculate the mass defect (\( \Delta m \)).
The mass defect is the difference between the initial and final masses:
\[ \Delta m = m_{\text{initial}} - m_{\text{final}} = 236.05258 \, u - 235.85852 \, u = 0.19406 \, u \]

### Step 5: Convert the mass defect to energy using \( E = \Delta m c^2 \).
To convert the mass defect into energy, we use the conversion factor \( 1 \, u = 931.5 \, \text{MeV}/c^2 \):
\[ E = \Delta m \cdot 931.5 \, \text{MeV} = 0.19406 \, u \cdot 931.5 \, \text{MeV}/c^2 \]
Calculating the energy:
\[ E \approx 0.19406 \cdot 931.5 \approx 181.0 \, \text{MeV} \]

### Final Answer:
The energy released in the fission reaction is approximately **181 MeV**.

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