Bohr's Model Radius Calculation NEET Cheat Sheet: Everything You Need

What NEET Asks

• Direct application of Bohr's radius formula for hydrogen and hydrogen-like species.
• Questions on proportionality of radius with principal quantum number (n) and atomic number (Z).
• Comparative analysis of radii for different orbits or species. Expected 1-2 questions, generally easy to medium, testing either direct formula application or comparative analysis.

Key Points

• Bohr's model applies only to single-electron species (H, He$^+$, Li$^{2+}$, Be$^{3+}$).
• The electron revolves in fixed circular orbits called stationary states, without radiating energy.
• Angular momentum is quantized: mvr = nħ (where ħ = h/2π).
• The radius of the nth orbit is derived by equating centripetal force and electrostatic force.
• The first Bohr radius for hydrogen (n=1, Z=1), denoted as $a_0$, is 0.529 Å or 52.9 pm.

Must-Know Formula / Reaction

$r_n = 0.529 \times \frac{n^2}{Z} \text{ Å}$ Where:

• $r_n$: Radius of the nth orbit
• $n$: Principal quantum number (integer representing the orbit number)
• $Z$: Atomic number of the hydrogen-like species

Common Mistakes

• Students often forget to square 'n' in the formula. Remember it's $n^2$, not just $n$.
• Don't confuse 'Z' (atomic number) with the number of electrons. The formula uses Z for the nuclear charge.
• Incorrectly applying the formula to multi-electron species or atoms; it's strictly for H-like species only.

Rapid Revision

Bohr's radius for H-like species: $r_n = 0.529 \times (n^2/Z)$ Å. Remember the proportionality $r_n \propto n^2/Z$. Quickly recall this proportionality and the constant for direct problem solving and ratio-based questions.