Consider an `alpha`-particle just in contact with `.""_(92)^(238)U` nucleus. Calculate the coulombic repulsion energy (i.e., the height of the coulombic barrier between `""^(238)U` and the `alpha`-particle) assuming that the distance between them is equal to the sum of their radii. (`r_(0)= 1.4 xx 10^(-13), e= 4.8 xx 10^(-10)` esu)

Explanation

To calculate the Coulombic repulsion energy between an alpha particle and a Uranium-238 nucleus, we will follow these steps:

### Step 1: Calculate the radius of the Uranium-238 nucleus
The radius \( r \) of a nucleus can be estimated using the formula:
\[ r = r_0 \cdot A^{1/3} \]
where \( r_0 = 1.4 \times 10^{-13} \) cm and \( A \) is the mass number.
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