Cornell Note: Bohr's Model of the Atom

type: cornell_note | subtopic: Bohr Model

Cue Column | Note-Taking Area

Cue	Notes
Postulate 1	Electrons move in fixed circular orbits (stationary states) without radiating energy. Defies classical EM (accelerating charges should radiate).
Postulate 2	Angular momentum quantized: L = nℏ = nh/(2π), n = 1, 2, 3, …
Postulate 3	Energy emitted/absorbed as photon during transitions: E = hν = Ei − Ef
Orbital radius formula	r_n = a_{0} $n^{2}$ /Z where a_{0} = 0.529 Å. Radius ∝ $n^{2}$ /Z
Velocity formula	v_n = $2.18 \times 10^{6}$ Z/n m/s. Velocity ∝ Z/n
Energy formula	E_n = −13.6 $Z^{2}$ / $n^{2}$ eV. Energy ∝ − $Z^{2}$ / $n^{2}$
KE and PE relations	KE = −E_n (positive); PE = 2E_n (negative); KE + PE = E_n
Period of revolution	T_n ∝ $n^{3}$ / $Z^{2}$
Limitation	Works only for H and H-like single-electron ions ( $He^{+}$ , $Li^{2+}$ , $Be^{3+}$ ).
Where it fails	Multi-electron atoms (He, Li, etc.); Zeeman/Stark effects; fine structure

Key Values for H (Z=1):

n	r_n (Å)	v_n (×10^{6} m/s)	E_n (eV)	KE (eV)	PE (eV)
1	0.529	2.18	−13.6	+13.6	−27.2
2	2.116	1.09	−3.4	+3.4	−6.8
3	4.761	0.727	−1.511	+1.511	−3.022
4	8.464	0.545	−0.85	+0.85	−1.70

Summary:

Bohr introduced quantum conditions into atomic structure. The three postulates resolve the instability of Rutherford's model. Electrons stay in stationary orbits with quantized angular momentum and emit photons only during level transitions.