( Atomic \ Structure)

$Atomic \ Structure$

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$ Magnetic \ Quantum \ Number$ $ (m / m_l) $

$ Spin \ Quantum \ Number$ $ ( m_s / s) $

$ 3D \ Shape$

$ l = 0 $ $ to $ $ (n-1) $

Max

$ Orbitals = \ 2l + 1 $

$ e^- $ $ = 2(2l + 1) $

$ ( l )$ = $ \frac{0}{s} $$ \frac{1}{p} $$ \frac{2}{d} $$ \frac{3}{f} $$ \frac{4}{g} $

$ Orientation \ Of \ Orbital$

$ m = -l $ $ to $ $ +l $

$ Total $$ Orbitals$ $ =$ $ \Sigma^{n-1}_{l=0} (2l+1)$

$ Spin \ of \ e^- $

$ m = $ $ \frac{+1}{2} $$ or $ $ \frac{-1}{2} $

$ Total$ $ Spin = $ $ S = $ $ \frac{+n}{2} $ $ or $ $ \frac{-n}{2} $

$ Total$ $ Spin $ $ Multiplicity = $ $ 2S + 1 $

$ Spin$ $ Magnetic$ $ Moment = $ $ μ_s = $ $ \surd n(n+2) $

$ Magnetic$ $ Moment = $ $ μ = $ $ \surd n(n+2) $ $ B.M $

$ Paramagnetic$

$ Dimagnetic$

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$ Bohr's \ Atomic \ Model$

$ Planck's \ Quantum \ Theory$

$ Quantum = 1$

$ Quanta = Many$

$ 1 \ ev \ atom^{-1} = 96.33 \ kJ \ mol^{-1} = 23 \ kCal \ mol^{-1} $

$ E = nhc/λ \ ≈ 12400 / λ (Ang) $

$ Light = Photon$

$ Formulae$

$ Velocity $

$ Radius $

$ r = $$ 52.9 \frac{n^2 }{ Z} \ pm\ or \ 0.529 \frac{n^2 }{ Z} \ Ang$

$ V = $$ 2.18 * 10^6 \frac{Z }{ n} \ m \ s^{-1}$

$Energy $

$ E = $$ -2.18 * 10^{-18} \frac{Z^2}{n^2} \ J \ atom^{-1}$

$ or \ E = $$ -13.6 \frac{Z^2}{n^2} \ ev \ atom^{-1}$

$PE = 2(TE) = -2(KE)$

$a_0 = 52.9 \ pm \ or \ 0.529 Ang$

$Time \ Period \ of \ Rev. $

$ T = $$ \frac{2 \ \pi \ r_0 }{V_0}$ * $ \frac{n^3}{Z^2} \ sec$

$Frequency $

$ \frac{1}{T} $

$ Size \ and \ Radius \ of \ Atom$

$ R = R_0 \ (A)^{1/3}$

$ 1808$

$ Quantum \ Mechanical \ Model$

$ Quantum \ Numbers$

$ 1. Principal \ Quantum \ Number$ $ ( n )$

$ Max$

$ Identify \ Shell$

$ n = $$ \frac{1}{K} $$ \frac{2}{L} $$ \frac{3}{M} $$ \frac{4}{N} $

$ +ve \ Values$

$ 1904$

$ Dalton's \ Atomic \ Model$

$ Laws$

$ Law \ of \ Constant \ Proportions$

$Postulates$

$ Limitations$

$ Indivisible $

$ Same \ or \ Not$

$ Same \ Element = Identical$

$ Different \ Element = Different$

$ Chemical \ Reactions = Reorganization$

$ Combine = Fixed \ Whole \ No. \ Ratio$

$ Isotopes$

$ Isobars$

$ Sub - Atomic \ Particles$

$ Complex \ Organic \ Compounds - Not \ Always \ Whole \ No. \ Ratio$

$ Allotropes$

$ Billiard \ Ball \ Model$

$ Plum \ Pudding \ Model$

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$ r = $$ \frac{n^2 \ h^2}{4 \pi^2 \ m \ K \ Z \ e^2} $

$ Orbitals = \ n^2 $

$ Law \ Conservation \ of \ Mass$

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$Proton \ / \ Electron$

$ Electrons \ (e^-)$

$ 1911$

$ h = 6.626 * 10^-34$

$ 1897$

$ The \ Cathode \ Ray \ Tube \ Experiment$

$ Result$

$ Experiment$

$ 1886$

$ The \ Anode \ Ray \ Tube \ Experiment$

$ Observation$

$ Result$

$ Experiment$

$ Observation$

$ e^- $ $ = 2n^2 $

$ Define-\ e^- $

$ Subshells = n $

$ 2.Subsidiary / Azimuthal / Orbital \ Angular \ Momentum \ Quantum \ Numbers$ $ ( l )$

$ Nuclear \ Model$

$ 1911$

$The \ Gold \ Foil \ Experiment - Nucleus $

$ Observation$

$ Result$

$ Distance \ of \ Closest \ Approach$

$ r = $$ 0.137964 \frac{z^2}{v^2} $

$r = 2 \frac{ k \ z_1 \ z_2 \ e^2}{m \ v^2}$

$ Experiment$

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