Calcualte the excitation energy of the compound nuclei produced when
Given:
`{:(M(.^(235)U) = 235.0439 "amu"",",M(n) = 1.0087 "amu"","),(M(.^(238)U)238.0508 "amu,",M(.^(236)U) = 236.0456 "amu,"),(M(.^(239)U) = 239.0543 "amu",):}`.

Explanation

To calculate the excitation energy of the compound nuclei produced in the reactions involving Uranium isotopes and neutrons, we can follow these steps:

### Step 1: Identify the Reactions
We have two reactions:
1. \( n + {}^{235}\text{U} \rightarrow {}^{236}\text{U}^* \)
2. \( n + {}^{238}\text{U} \rightarrow {}^{239}\text{U}^* \)

### Step 2: Write the Formula for Excitation Energy
The excitation energy \( E^* \) of the compound nucleus can be calculated using the formula:
\[ E^* = (M_n + M_{A}) - M_{A^*} \times c^2 \]
where:
- \( M_n \) is the mass of the neutron,
- \( M_{A} \) is the mass of the target nucleus (Uranium isotope),
- \( M_{A^*} \) is the mass of the compound nucleus,
- \( c \) is the speed of light (we will use \( c^2 \) in MeV/amu).

### Step 3: Calculate the Excitation Energy for the First Reaction
For the first reaction:
- \( M_n = 1.0087 \, \text{amu} \)
- \( M_{235\text{U}} = 235.0439 \, \text{amu} \)
- \( M_{236\text{U}} = 236.0456 \, \text{amu} \)

Plugging these values into the formula:
\[ E^*_{236} = (1.0087 + 235.0439) - 236.0456 \times 931.5 \]
Calculating:
\[ E^*_{236} = (236.0526 - 236.0456) \times 931.5 \]
\[ E^*_{236} = 0.007 \times 931.5 \approx 6.5 \, \text{MeV} \]

### Step 4: Calculate the Excitation Energy for the Second Reaction
For the second reaction:
- \( M_{238\text{U}} = 238.0508 \, \text{amu} \)
- \( M_{239\text{U}} = 239.0543 \, \text{amu} \)

Plugging these values into the formula:
\[ E^*_{239} = (1.0087 + 238.0508) - 239.0543 \times 931.5 \]
Calculating:
\[ E^*_{239} = (239.0595 - 239.0543) \times 931.5 \]
\[ E^*_{239} = 0.0052 \times 931.5 \approx 4.8 \, \text{MeV} \]

### Step 5: Conclusion
From the calculations:
- The excitation energy for the first reaction (\( {}^{236}\text{U}^* \)) is approximately \( 6.5 \, \text{MeV} \).
- The excitation energy for the second reaction (\( {}^{239}\text{U}^* \)) is approximately \( 4.8 \, \text{MeV} \).

Thus, \( {}^{236}\text{U}^* \) has a higher excitation energy than \( {}^{239}\text{U}^* \).

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