The electrostatic potential energy between two identical nuclei produced in the fission on of `._(92)^(238)U` at the moment of their separation is `x` then find `x//180`. Given `R_(0)=1.3xx10^(-15)m` and `epsilon_(0)=8.85xx10^(-12)Fm^(-1)`.

Answer

To solve the problem of calculating the electrostatic potential energy between two identical nuclei produced in the fission of \( _{92}^{238}U \), we will follow these steps:

### Step 1: Determine the Charge of Each Nucleus
The charge of a nucleus is given by the formula:
\[ Q = Z \cdot e \]
where \( Z \) is the atomic number and \( e \) is the elementary charge (\( e = 1.6 \times 10^{-19} \, C \)).

For uranium, the atomic number \( Z = 92 \). After fission, each nucleus will have:
\[ Z' = \frac{92}{2} = 46 \]
Thus, the charge of each nucleus is:
\[ Q = 46 \cdot (1.6 \times 10^{-19}) = 7.36 \times 10^{-18} \, C \]

### Step 2: Calculate the Radius of Each Nucleus
The radius of a nucleus can be estimated using the formula:
\[ R = R_0 \cdot A^{1/3} \]
where \( R_0 = 1.3 \times 10^{-15} \, m \) and \( A \) is the mass number.

For each nucleus after fission, the mass number is:
\[ A' = \frac{238}{2} = 119 \]
Thus, the radius is:
\[ R = 1.3 \times 10^{-15} \cdot (119)^{1/3} \]
Calculating \( (119)^{1/3} \):
\[ (119)^{1/3} \approx 4.92 \]
So,
\[ R \approx 1.3 \times 10^{-15} \cdot 4.92 \approx 6.396 \times 10^{-15} \, m \]

### Step 3: Calculate the Distance Between the Two Nuclei
Since we are considering the separation at the moment they are just about to separate, the distance \( d \) between the two nuclei is:
\[ d = 2R \approx 2 \cdot 6.396 \times 10^{-15} \approx 1.2792 \times 10^{-14} \, m \]

### Step 4: Calculate the Electrostatic Potential Energy
The electrostatic potential energy \( U \) between two point charges is given by:
\[ U = \frac{k \cdot Q_1 \cdot Q_2}{d} \]
where \( k \) is Coulomb's constant (\( k = 9 \times 10^9 \, N \cdot m^2/C^2 \)).

Since \( Q_1 = Q_2 = Q \):
\[ U = \frac{k \cdot Q^2}{d} \]
Substituting the values:
\[ U = \frac{9 \times 10^9 \cdot (7.36 \times 10^{-18})^2}{1.2792 \times 10^{-14}} \]
Calculating \( (7.36 \times 10^{-18})^2 \):
\[ (7.36 \times 10^{-18})^2 \approx 5.41 \times 10^{-35} \]
Now substituting:
\[ U \approx \frac{9 \times 10^9 \cdot 5.41 \times 10^{-35}}{1.2792 \times 10^{-14}} \approx \frac{4.87 \times 10^{-25}}{1.2792 \times 10^{-14}} \approx 3.81 \times 10^{-11} \, J \]

### Step 5: Convert to Electron Volts
To convert joules to electron volts, use the conversion factor \( 1 \, eV = 1.6 \times 10^{-19} \, J \):
\[ U \approx \frac{3.81 \times 10^{-11}}{1.6 \times 10^{-19}} \approx 238.125 \, MeV \]

### Step 6: Calculate \( \frac{x}{180} \)
Now we need to find \( \frac{x}{180} \):
\[ \frac{x}{180} = \frac{238.125}{180} \approx 1.322 \]

### Final Answer
Thus, the value of \( \frac{x}{180} \) is approximately:
\[ \boxed{1.322} \]