A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic charge. It makes a closest approach of `10fm` to the nucleus. The de - Broglie wavelength (in units of fm) of the proton at its start is take the proton mass, `m_p = 5//3xx10^(-27) kg, h//e = 4.2xx10^(-15) J-s//C`, `(1)/(4piepsilon_0) = 9xx10^9m //F, 1 fm = 10^(-15)`.

Explanation

To find the de Broglie wavelength of a proton fired towards a nucleus with charge \( Q = 120e \) and making a closest approach of \( 10 \, \text{fm} \), we will follow these steps:

### Step 1: Understand the Conservation of Energy
The kinetic energy of the proton when it is far away from the nucleus is converted into electrostatic potential energy at the closest approach. Thus, we can write:
\[ \text{K.E.} = \text{Potential Energy} \]
\[
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