The binding energy per each nucleon in the neighborhood of medium nuclei is `8.5` MeV and the binding energy per each nucleon is about `7.6` MeV and the neighborhood of Uranium. The energy released in the fission of `U ^(236)` is

Options

A. 212 eV
B. 212 MeV
C. `2.12` MeV
D. `0.9` MeV

Explanation

To find the energy released in the fission of Uranium-236, we can follow these steps:

### Step 1: Understand the Binding Energy
The binding energy per nucleon for medium nuclei is given as \(8.5 \, \text{MeV}\), and for Uranium, it is \(7.6 \, \text{MeV}\). This implies that medium nuclei are more stable than Uranium nuclei.

### Step 2: Calculate the Total Binding Energy of Uranium-236
The total binding energy of Uranium-236 can be calculated using the formula:
\[ \text{Total Binding Energy of } U^{236} = \text{Binding Energy per Nucleon} \times \text{Number of Nucleons} \]
Given that the number of nucleons in Uranium-236 is 236, we can calculate:
\[ \text{Total Binding Energy of } U^{236} = 7.6 \, \text{MeV/nucleon} \times 236 \, \text{nucleons} = 1793.6 \, \text{MeV} \]

### Step 3: Calculate the Total Binding Energy of the Fission Products
When Uranium-236 undergoes fission, it produces medium nuclei. The binding energy per nucleon for these medium nuclei is \(8.5 \, \text{MeV}\). Assuming that the fission results in two medium nuclei, the total binding energy of the products can be calculated as:
\[ \text{Total Binding Energy of Products} = 8.5 \, \text{MeV/nucleon} \times 236 \, \text{nucleons} = 2006 \, \text{MeV} \]

### Step 4: Calculate the Energy Released in Fission
The energy released in the fission process can be calculated by finding the difference between the total binding energy of the products and the total binding energy of the reactants (Uranium-236):
\[ \text{Energy Released} = \text{Total Binding Energy of Products} - \text{Total Binding Energy of } U^{236} \]
Substituting the values we calculated:
\[ \text{Energy Released} = 2006 \, \text{MeV} - 1793.6 \, \text{MeV} = 212.4 \, \text{MeV} \]

### Final Answer
The energy released in the fission of \(U^{236}\) is approximately \(212.4 \, \text{MeV}\).

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