Show that the radius of the orbit in hydrogen atom varies as n2, where n is the principal quantum number of the atom.

Explanation

To show that the radius of the orbit in a hydrogen atom varies as \( n^2 \), where \( n \) is the principal quantum number, we can use the Bohr model of the hydrogen atom. Here is a step-by-step solution:

### Step 1: Understand the Forces Acting on the Electron
In a hydrogen atom, the electron is attracted to the nucleus (proton) by the electrostatic force. According to Coulomb's law, the electrostatic force \( F \) between the electron and the proton is given by:
\[ F = \frac{k \cdot e^2}{r^2} \]
where:
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