Radius Of Nth Bohr Orbit — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Radius of nth Bohr Orbit Hydrogen-like atoms (single-electron species such as H, He+, Li++). Equate Coulomb force to Centripetal force: kZe²/r² = mv²/r Apply Bohr's quantization of angular momentum: mvr = nh/(2π) Solve the momentum equation for velocity: v = nh/(2πmr) Substitute v into the force equation and solve for r Result: r = (ε₀n²h²)/(πmZe²) Substitute physical constants to get r ≈ 0.529 n²/Z Å Only applicable to single-electron species. Assumes circular orbits (Bohr model approximation). Nucleus is assumed to be infinitely heavy (stationary) in the simplified derivation. Thinking the radius scales linearly with n (it scales with n²). Applying this formula to multi-electron atoms like neutral Helium. Forgetting that the result is in Angstroms, not meters.