Velocity Of Electron In Nth Orbit Bohr Model — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Velocity of Electron in nth Orbit (Bohr Model) Applicable only to hydrogen-like atoms (single-electron species such as H, He+, Li++, etc.) within the context of the Bohr Model. Assume Bohr's quantization of angular momentum: mvr = nh / (2π). Equate centripetal force to electrostatic Coulomb force: mv²/r = (kZe²)/r². Divide the force equation by the velocity equation to eliminate radius r. Isolate v to get v = (kZe²2π) / (nh). Substitute standard constants (k, e, h) to obtain the numerical constant ≈ 2.18 × 10 6 m/s. The atom/ion must have only one electron. n must be a positive integer. Relativistic effects are ignored (valid for low Z). Treats electron orbit as circular. Believing velocity increases with the orbit number n (it actually decreases as 1/n). Confusing the dependency of velocity (∝ Z/n) with energy (∝ Z²/n²) or radius (∝ n²/Z). Applying the formula to multi-electron atoms like neutral Helium.