According to Bohr's principle, the relation between atomic radius (r) and principal quantum number (n) is given by?

1. Atomic Radius (r):
   The distance between the nucleus and the electron in a specific orbit.

2. Principal Quantum Number (n):
   Denotes the orbit number (n = 1, 2, 3, ...) where the electron resides.

3. Bohr Radius (a₀):
   The smallest possible radius of the hydrogen atom's orbit, approximately equal to 0.529 Å (angstroms).

4. Formula Derivation:
   According to Bohr's model:

   • The radius of the nth orbit is proportional to n2n^2n2, where $n$ is the principal quantum number.
   • Hence, rn=n2a0r_n = n^2 a_0rn​=n2a0​, where a0a_0a0​ is the Bohr radius.

Key Insights:

• Direct Relationship: As $n$ increases, the atomic radius rnr_nrn​ increases quadratically.
• Hydrogen-like Atoms: For single-electron species such as He+^++, Li2+^{2+}2+, etc., the formula modifies to:rn=n2a0Zr_n = \frac{n^2 a_0}{Z}rn​=Zn2a0​​where $Z$ is the atomic number.

This relationship is fundamental in understanding the structure of atoms and their energy levels in quantum mechanics.