Prove that `u_(n) = sqrt((Zn^(2))/(mr_(n)))` where n is the Z at distance r_(n) from the m and r mass and charge of electron

Explanation

To prove that \( u_n = \sqrt{\frac{Z n^2}{m r_n}} \), where \( n \) is the atomic number \( Z \) at a distance \( r_n \) from the mass \( m \) and charge of the electron, we can follow these steps:

### Step 1: Understand the Forces Acting on the Electron
In a circular orbit, the electron experiences two main forces:
1. **Electrostatic Force (Coulomb's Law)**: This force acts between the positively charged nucleus (with charge \( Ze \)) and the negatively charged electron.
2. **Centripetal Force**: This force is required to keep the electron in circular motion.

### Step 2: Write the Electrostatic Force Equation
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