Atomic Models — Revision Notes

⚡ 30-Second Revision

Dalton: — Indivisible spheres.
Thomson: — Plum pudding, positive sphere with embedded electrons.
Rutherford: — Nuclear model, tiny dense positive nucleus, electrons orbit. Limitations: stability, line spectra.
Bohr: — Quantized orbits ($n=1,2,3...$), no energy radiation in orbits.
Angular Momentum: — $m_e v r = n \frac{h}{2\pi}$
Radius: — $r_n = 0.529 \times \frac{n^2}{Z}$ Å
Energy: — $E_n = -13.6 \times \frac{Z^2}{n^2}$ eV
Velocity: — $v_n = 2.18 \times 10^6 \times \frac{Z}{n}$ m/s
Rydberg Formula: — $\frac{1}{\lambda} = R_H Z^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$
Spectral Series: — Lyman ($n_1=1$, UV), Balmer ($n_1=2$, Visible), Paschen ($n_1=3$, IR).

2-Minute Revision

Atomic models describe the atom's internal structure, evolving from simple ideas to complex quantum theories. Dalton's model proposed indivisible atoms. Thomson's 'plum pudding' model introduced electrons embedded in a positive sphere. Rutherford's alpha-scattering experiment revealed the dense, positive nucleus, with electrons orbiting it (nuclear model). However, Rutherford's model failed to explain atomic stability and line spectra.

Bohr's model addressed these issues for hydrogen. Its key postulates include: electrons exist in specific, quantized 'stationary orbits' without radiating energy; angular momentum is quantized ($m_e v r = n h/(2\pi)$); and energy is absorbed/emitted only during transitions between orbits.

Bohr's model successfully derived formulas for orbital radius ($r_n \propto n^2/Z$), electron energy ($E_n \propto -Z^2/n^2$), and explained the hydrogen line spectrum using the Rydberg formula. Its limitations include failure for multi-electron atoms and inability to explain fine structure or Zeeman/Stark effects.

5-Minute Revision

The journey of atomic models highlights scientific progress. Dalton's theory (1808) established atoms as fundamental, indivisible particles. The discovery of the electron led J.J. Thomson (1904) to propose the 'plum pudding' model, where electrons were embedded in a uniform positive sphere.

This was disproven by Rutherford's (1911) alpha-particle scattering experiment, which showed most alpha particles passed through, but a few were deflected at large angles, indicating a tiny, dense, positively charged nucleus at the atom's center, with electrons orbiting it – the nuclear model.

Rutherford's model, however, couldn't explain why electrons didn't spiral into the nucleus (atomic stability) or why atoms emit discrete line spectra.

Niels Bohr (1913) resolved these issues for the hydrogen atom by introducing quantum concepts. His postulates were: 1) Electrons orbit in specific 'stationary states' or energy levels without radiating energy.

2) The angular momentum of an electron is quantized, $m_e v r = n \frac{h}{2\pi}$. 3) Energy is absorbed or emitted only when an electron jumps between these allowed orbits, with $\Delta E = h\nu$. Bohr's model successfully derived expressions for the radius ($r_n = 0.

529 \times \frac{n^2}{Z}$Å), energy ($E_n = -13.6 \times \frac{Z^2}{n^2}$eV), and velocity ($v_n = 2.18 \times 10^6 \times \frac{Z}{n}$m/s) for hydrogen-like species. It also explained the hydrogen spectrum using the Rydberg formula:$\frac{1}{\lambda} = R_H Z^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$, categorizing transitions into series like Lyman ($n_1=1$, UV) and Balmer ($n_1=2$, Visible).

Key limitations of Bohr's model include its failure for multi-electron atoms, inability to explain spectral line intensities, fine structure, or the Zeeman/Stark effects, and its classical treatment of electrons as particles in fixed orbits.

Prelims Revision Notes

1
Dalton's Atomic Theory (1808): — Atoms are indivisible, indestructible, identical for an element, combine in simple ratios. Limitations: No subatomic particles, isotopes.
2
Thomson's Plum Pudding Model (1904): — Positive sphere with embedded electrons. Limitations: Failed Rutherford's experiment.
3
Rutherford's Nuclear Model (1911):

* Experiment: Alpha-particle scattering on gold foil. * Observations: Most pass through, some small deflections, very few large deflections/bounce back. * Conclusions: Atom mostly empty space, dense positive nucleus at center, electrons orbit. * Limitations: Atomic instability (electrons should spiral into nucleus), couldn't explain line spectra.

1
Bohr's Atomic Model (1913) (for H-like species):

* Postulates: * Electrons in specific, stable 'stationary orbits' (energy levels) without radiating energy. * Angular momentum is quantized: $m_e v r = n \frac{h}{2\pi}$ ($n=1,2,3...$ is principal quantum number).

* Energy absorbed/emitted only during transitions between orbits: $\Delta E = E_{final} - E_{initial} = h\nu$. * Key Formulas: * Radius: $r_n = 0.529 \times \frac{n^2}{Z}$ Å. ($r_n \propto n^2/Z$) * Energy: $E_n = -13.

6 \times \frac{Z^2}{n^2}$eV/atom. ($E_n \propto -Z^2/n^2$) * **Velocity:**$v_n = 2.18 \times 10^6 \times \frac{Z}{n}$m/s. ($v_n \propto Z/n$) * **Spectral Lines (Rydberg Formula):**$\frac{1}{\lambda} = \bar{\nu} = R_H Z^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$*$R_H = 1.

097 \times 10^7 \text{ m}^{-1}$(Rydberg constant) *$n_1$: lower orbit,$n_2$: higher orbit ($n_2 > n_1$) * **Spectral Series for Hydrogen ($Z=1$):** * **Lyman:**$n_1=1$,$n_2=2,3,4...$, UV region.

* Balmer: $n_1=2$, $n_2=3,4,5...$, Visible region. * Paschen: $n_1=3$, $n_2=4,5,6...$, Infrared region. * Brackett: $n_1=4$, $n_2=5,6,7...$, Infrared region. * Pfund: $n_1=5$, $n_2=6,7,8...

$, Infrared region. * Limitations: Failed for multi-electron atoms, couldn't explain fine structure, Zeeman/Stark effects, wave nature of electron, Heisenberg Uncertainty Principle.

Vyyuha Quick Recall

To remember the order of atomic models and their key features:

Don't Think Really Bad Questions

Dalton: Divisible? No, Dense spheres.
Thomson: Tiny electrons in Thick positive pudding.
Rutherford: Really empty space, Really small nucleus, Really unstable orbits.
Bohr: Bound electrons in Basic quantized orbits, Bright line spectra.
Quantum: Quite complex, Quantum numbers, Quantum mechanics (the next step beyond Bohr).