Structure of Atom — Revision Notes

⚡ 30-Second Revision

Subatomic Particles: — Proton ($+1e$, in nucleus), Neutron (neutral, in nucleus), Electron ($-1e$, orbits nucleus).
Atomic Number (Z): — Number of protons. Defines element.
Mass Number (A): — Protons + Neutrons.
Isotopes: — Same Z, different A (different neutrons).
Bohr's Model: — Fixed orbits, quantized energy ($E_n = -13.6 \times Z^2/n^2 \text{ eV}$), quantized angular momentum ($mvr = n h/2pi$). Fails for multi-electron atoms.
Quantum Mechanical Model: — Orbitals (probability regions), wave-particle duality ($lambda = h/mv$), Uncertainty Principle ($Delta x cdot Delta p ge h/4pi$).
Quantum Numbers:

* $n$: Principal (energy, size), $1, 2, 3, ...$ * $l$: Azimuthal (shape, subshell), $0$ to $n-1$ (s, p, d, f). * $m_l$: Magnetic (orientation), $-l$ to $+l$. * $m_s$: Spin (electron spin), $pm 1/2$.

Orbital Capacity: — Max 2 electrons/orbital (Pauli).
Subshell Capacity: — $2(2l+1)$ electrons.
Shell Capacity: — $2n^2$ electrons.
Electron Filling Rules:

* Aufbau: Fill lowest energy orbitals first. * Pauli: No two electrons same 4 quantum numbers. * Hund's: Degenerate orbitals filled singly with parallel spins first.

Rydberg Formula (H-like): — rac{1}{lambda} = R_H Z^2 left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) ($R_H = 1.097 \times 10^7 \text{ m}^{-1}$).
Exceptions (Aufbau): — Cr ($[Ar]3d^5 4s^1$), Cu ($[Ar]3d^{10} 4s^1$).

2-Minute Revision

The atom, the basic unit of matter, comprises a positively charged nucleus (protons and neutrons) surrounded by negatively charged electrons. The atomic number (Z) defines the element, while the mass number (A) is the sum of protons and neutrons.

Isotopes are atoms of the same element with different neutron counts. Early models by Rutherford established the nuclear atom, but Bohr's model, with its quantized orbits and energy levels, explained the hydrogen spectrum.

Its limitations for multi-electron atoms paved the way for the quantum mechanical model.

This modern model describes electrons in probabilistic regions called orbitals, governed by four quantum numbers: principal ($n$, energy/size), azimuthal ($l$, shape/subshell), magnetic ($m_l$, orientation), and spin ($m_s$, electron spin).

Electrons fill these orbitals according to the Aufbau principle (lowest energy first), Pauli Exclusion Principle (max two electrons per orbital with opposite spins), and Hund's Rule (single occupancy with parallel spins in degenerate orbitals before pairing).

Atomic spectra, particularly for hydrogen, are explained by electron transitions between quantized energy levels, calculable using the Rydberg formula. Remember exceptions to electron configuration like Cr and Cu due to enhanced stability of half-filled or fully-filled d-orbitals.

5-Minute Revision

The structure of an atom is central to chemistry. It begins with the nucleus, a dense core of positively charged protons (defining the element, Z) and neutral neutrons. Electrons, with negative charge, orbit this nucleus.

The total number of protons and neutrons gives the mass number (A). Atoms of the same element with different neutron counts are called isotopes. Early models progressed from Dalton's indivisible spheres to Thomson's plum pudding, then Rutherford's nuclear model, which established the tiny, dense nucleus.

However, Rutherford's model couldn't explain atomic stability or line spectra.

Bohr's model introduced quantized, fixed orbits where electrons don't radiate energy, and their angular momentum is quantized ($mvr = n h/2pi$). This successfully explained the hydrogen spectrum, with electron transitions between energy levels ($E_n = -13.6 \times Z^2/n^2 \text{ eV}$) causing specific spectral lines, calculable via the Rydberg formula. However, Bohr's model failed for multi-electron atoms and couldn't explain phenomena like the Zeeman effect.

The quantum mechanical model, the current accepted view, incorporates de Broglie's wave-particle duality ($lambda = h/mv$) and Heisenberg's Uncertainty Principle ($Delta x cdot Delta p ge h/4pi$). It describes electrons in three-dimensional probability regions called atomic orbitals, not fixed paths.

Each electron's state is uniquely defined by four quantum numbers: $n$ (principal, energy/size, $1,2,3...$), $l$ (azimuthal, shape/subshell, $0$ to $n-1$), $m_l$ (magnetic, orientation, $-l$ to $+l$), and $m_s$ (spin, $pm 1/2$).

Electrons fill these orbitals following three key rules: Aufbau Principle (lowest energy orbitals first, e.g., $1s < 2s < 2p < 3s < 3p < 4s < 3d$), Pauli Exclusion Principle (max two electrons per orbital with opposite spins), and Hund's Rule (for degenerate orbitals, fill singly with parallel spins before pairing).

Remember exceptions like Chromium ($[Ar]3d^5 4s^1$) and Copper ($[Ar]3d^{10} 4s^1$) due to the stability of half-filled or fully-filled d-orbitals. Mastering these rules is crucial for predicting electron configurations and understanding chemical properties.

Prelims Revision Notes

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Subatomic Particles: — Protons ($p^+$), Neutrons ($n^0$), Electrons ($e^-$). Protons and neutrons are in the nucleus. Electrons orbit. $p^+$ and $n^0$ have similar mass (approx. 1 amu), $e^-$ is much lighter.
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Atomic Number (Z): — Number of protons. Defines the element. In a neutral atom, $Z = \text{number of electrons}$.
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Mass Number (A): — Number of protons + number of neutrons. $A = Z + N$.
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Isotopes: — Same Z, different N (e.g., $^1H, ^2H, ^3H$).
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Isobars: — Different Z, same A (e.g., $^{40}Ar, ^{40}Ca$).
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Isotones: — Different Z, same N (e.g., $^{14}C_8, ^{15}N_8$).
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Bohr's Model:

* Electrons in fixed, circular orbits (stationary states). * Energy of orbits is quantized: $E_n = -13.6 \times Z^2/n^2 \text{ eV/atom}$. * Angular momentum is quantized: $mvr = n h/2pi$. * Explains H-spectrum, fails for multi-electron atoms.

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Quantum Mechanical Model:

* De Broglie's Hypothesis: Matter has wave-particle duality, $lambda = h/mv$. * Heisenberg's Uncertainty Principle: Cannot simultaneously know position and momentum of electron precisely, $Delta x cdot Delta p ge h/4pi$. * Atomic Orbital: 3D region of space where probability of finding electron is maximum (from Schrödinger equation).

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Quantum Numbers:

* **Principal ($n$):** $1, 2, 3, ...$ (K, L, M shells). Determines energy and size. Max electrons in shell = $2n^2$. * **Azimuthal ($l$):** $0, 1, ..., n-1$ (s, p, d, f subshells). Determines shape. Max orbitals in subshell = $2l+1$. Max electrons in subshell = $2(2l+1)$. * **Magnetic ($m_l$):** $-l, ..., 0, ..., +l$. Determines orientation. * **Spin ($m_s$):** $+1/2$ or $-1/2$. Electron spin.

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Electron Filling Rules:

* Aufbau Principle: Fill lowest energy orbitals first. Order: $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, ...$ (use $(n+l)$ rule). * Pauli Exclusion Principle: No two electrons in an atom can have the same set of all four quantum numbers. Max 2 electrons per orbital, with opposite spins. * Hund's Rule: For degenerate orbitals, fill singly with parallel spins before pairing.

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Electron Configuration Exceptions: — Cr ($[Ar]3d^5 4s^1$), Cu ($[Ar]3d^{10} 4s^1$) due to stability of half-filled/fully-filled d-orbitals.
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Atomic Spectra (Hydrogen): — Emission/absorption of specific wavelengths. Rydberg formula: rac{1}{lambda} = R_H Z^2 left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right). $R_H = 1.097 \times 10^7 \text{ m}^{-1}$. Lyman ($n_1=1$, UV), Balmer ($n_1=2$, visible), Paschen ($n_1=3$, IR).

Vyyuha Quick Recall

All People Have Exceptions (for electron filling rules): Aufbau, Pauli, Hund's, and Exceptions (Cr, Cu).