📝 Chapter Notes & Revision

Structure of Atom

🏫 MP BoardClass 11Chemistry

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Quick Revision Notes & Formula Sheet

Class 11 Chemistry — Chapter 2: Structure of Atom (परमाणु की संरचना)

1. Fundamental Subatomic Particles

ParticleSymbolCharge (C)Mass (kg)Discovered By
Electron (इलेक्ट्रॉन)$e^-$$-1.602 \times 10^{-19}$$9.109 \times 10^{-31}$J.J. Thomson
Proton (प्रोटॉन)$p^+$$+1.602 \times 10^{-19}$$1.672 \times 10^{-27}$E. Goldstein
Neutron (न्यूट्रॉन)$n^0$$0$$1.674 \times 10^{-27}$J. Chadwick
  • Atomic Number ($Z$) = Number of protons = Number of electrons (in a neutral atom)
  • Mass Number ($A$) = Number of protons ($Z$) + Number of neutrons ($N$)
  • Isotopes (समस्थानिक): Same $Z$, different $A$ (e.g., $^1_1\text{H}, ^2_1\text{H}, ^3_1\text{H}$)
  • Isobars (समभारिक): Same $A$, different $Z$ (e.g., $^{40}{18}\text{Ar}, ^{40}{20}\text{Ca}$)
  • Isotones (समन्यूट्रॉनिक): Same number of neutrons ($A - Z$)
  • Isoelectronic Species: Species having the same number of electrons (e.g., $\text{Na}^+, \text{Mg}^{2+}, \text{F}^-, \text{Ne}$)

2. Wave Nature of Electromagnetic Radiation

  • Frequency ($\nu$): Number of waves passing through a point in one second. Unit: $\text{Hz}$ or $\text{s}^{-1}$.
  • Wavelength ($\lambda$): Distance between two consecutive crests or troughs. Unit: $\text{m}$ or $\text{\AA}$.
  • Wave Number ($\bar{\nu}$): Number of wavelengths per unit length. $$\bar{\nu} = \frac{1}{\lambda}$$
  • Speed of Light ($c$): $$c = \nu \cdot \lambda = 3 \times 10^8 \text{ m/s}$$

3. Planck's Quantum Theory & Photoelectric Effect

  • Energy of a Photon ($E$): $$E = h\nu = \frac{hc}{\lambda}$$ Where: $h = \text{Planck's constant} = 6.626 \times 10^{-34} \text{ J}\cdot\text{s}$

  • Total Energy for $n$ photons: $$E = n \cdot h\nu$$

  • Photoelectric Effect Equation: $$E = W_0 + \text{KE}_{\text{max}}$$ $$h\nu = h\nu_0 + \frac{1}{2}m_e v^2$$

    • $\nu_0$ = Threshold frequency (देहली आवृत्ति)
    • $W_0 = h\nu_0$ = Work function / Threshold energy (कार्य फलन)

4. Bohr's Atomic Model (For Single-Electron Species: $\text{H}, \text{He}^+, \text{Li}^{2+}$)

  1. Quantization of Angular Momentum: $$L = mvr = \frac{nh}{2\pi} \quad (n = 1, 2, 3, \dots)$$

  2. Radius of $n^{\text{th}}$ Orbit ($r_n$): $$r_n = 0.529 \times \frac{n^2}{Z} \text{ \AA} = 52.9 \times \frac{n^2}{Z} \text{ pm}$$

  3. Velocity of Electron in $n^{\text{th}}$ Orbit ($v_n$): $$v_n = 2.18 \times 10^6 \times \frac{Z}{n} \text{ m/s}$$

  4. Energy of Electron in $n^{\text{th}}$ Orbit ($E_n$): $$E_n = -2.18 \times 10^{-18} \times \frac{Z^2}{n^2} \text{ J/atom}$$ $$E_n = -13.6 \times \frac{Z^2}{n^2} \text{ eV/atom}$$

  5. Energy Transition ($\Delta E$): $$\Delta E = E_2 - E_1 = 2.18 \times 10^{-18} \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) Z^2 \text{ J}$$

5. Hydrogen Emission Spectrum

Rydberg Formula for calculating wave number of emitted radiation:

$$\bar{\nu} = \frac{1}{\lambda} = R_H \cdot Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$$

Where: $R_H = \text{Rydberg Constant} = 109,677 \text{ cm}^{-1} \approx 1.097 \times 10^7 \text{ m}^{-1}$

Spectral SeriesLower State ($n_1$)Upper State ($n_2$)Spectral Region
Lyman$1$$2, 3, 4, \dots$Ultraviolet (पराबैंगनी)
Balmer$2$$3, 4, 5, \dots$Visible (दृश्य प्रकाश)
Paschen$3$$4, 5, 6, \dots$Near Infrared (अवरक्त)
Brackett$4$$5, 6, 7, \dots$Mid Infrared
Pfund$5$$6, 7, 8, \dots$Far Infrared
  • Maximum number of spectral lines emitted: $$N = \frac{(n_2 - n_1)(n_2 - n_1 + 1)}{2}$$ (If electron jumps from level $n$ to ground state $n=1$, $N = \frac{n(n-1)}{2}$)

6. Dual Nature of Matter & Uncertainty Principle

  • de Broglie Wavelength ($\lambda$): $$\lambda = \frac{h}{p} = \frac{h}{m v} = \frac{h}{\sqrt{2 m (\text{KE})}}$$

  • de Broglie Wavelength for an Electron accelerated by potential $V$: $$\lambda = \frac{12.27}{\sqrt{V}} \text{ \AA}$$

  • Heisenberg's Uncertainty Principle (हाइजेनबर्ग का अनिश्चितता का सिद्धांत): $$\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$$ $$\Delta x \cdot (m \Delta v) \ge \frac{h}{4\pi}$$ Where: $\Delta x$ = uncertainty in position, $\Delta p$ = uncertainty in momentum, $\Delta v$ = uncertainty in velocity.

7. Quantum Mechanical Model & Quantum Numbers (क्वांटम संख्याएँ)

A. The Four Quantum Numbers:

  1. Principal Quantum Number ($n$):

    • Represents shell size and energy.
    • Values: $n = 1, 2, 3, 4, \dots$ (K, L, M, N...)
    • Total orbitals in shell = $n^2$
    • Max electrons in shell = $2n^2$

  2. Azimuthal / Orbital Angular Momentum Quantum Number ($l$):

    • Represents subshell shape.
    • Values: $l = 0 \text{ to } (n - 1)$
    • $l=0 \rightarrow s$ (Spherical)
    • $l=1 \rightarrow p$ (Dumbbell)
    • $l=2 \rightarrow d$ (Double dumbbell)
    • $l=3 \rightarrow f$ (Complex)
    • Orbital Angular Momentum: $L = \sqrt{l(l+1)} \frac{h}{2\pi} = \sqrt{l(l+1)} \hbar$

  3. Magnetic Quantum Number ($m_l$):

    • Represents orientation of orbitals in space.
    • Values: $m_l = -l \text{ to } +l$ (Total $= 2l + 1$ values)

  4. Spin Quantum Number ($m_s$):

    • Represents spin orientation of electron.
    • Values: $+\frac{1}{2}$ (Spin-up) or $-\frac{1}{2}$ (Spin-down)
    • Spin Angular Momentum: $S = \sqrt{s(s+1)} \frac{h}{2\pi}$

B. Nodes (नोड) and Nodal Planes:

  • Radial Nodes (Spherical Nodes): $= n - l - 1$
  • Angular Nodes (Nodal Planes): $= l$
  • Total Nodes: $= (n - l - 1) + l = n - 1$

8. Rules for Filling Orbitals in Atoms

  1. Aufbau Principle (आफ़बाऊ नियम):

    • Orbitals are filled in order of increasing energy based on the $(n + l)$ rule.
    • Lower $(n + l)$ value $\rightarrow$ Lower energy.
    • If two orbitals have the same $(n + l)$ value, the one with lower $n$ has lower energy.
    • Order: $1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d \dots$

  2. Pauli's Exclusion Principle (पाउली का अपवर्जन नियम):

    • No two electrons in an atom can have the same set of all four quantum numbers.
    • An orbital can accommodate a maximum of 2 electrons with opposite spins.

  3. Hund's Rule of Maximum Multiplicity (हुंड का अधिकतम बहुलता का नियम):

    • Electron pairing in degenerate orbitals ($p, d, f$) does not take place until each available orbital in that subshell is singly occupied with parallel spins.

9. Exceptional Electronic Configurations

Extra stability is associated with half-filled ($d^5, f^7$) and fully-filled ($d^{10}, f^{14}$) subshells due to symmetrical distribution and maximum exchange energy.

  • Chromium ($\text{Cr}$, $Z = 24$): $$\text{Expected: } [\text{Ar}] 3d^4 4s^2 \longrightarrow \textbf{Actual: } [\text{Ar}] 3d^5 4s^1$$
  • Copper ($\text{Cu}$, $Z = 29$): $$\text{Expected: } [\text{Ar}] 3d^9 4s^2 \longrightarrow \textbf{Actual: } [\text{Ar}] 3d^{10} 4s^1$$