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Formula Sheets / Chemistry

Chapter 2

Structure of Atom

Revise with flashcards Download this chapter (PDF) All Chemistry formulas (PDF)

Bohr's model for hydrogen-like species Dual nature and uncertainty Quantum mechanical model

Bohr's model for hydrogen-like species

$r_{n} = 0.529 \frac{n ^{2}}{Z}$ Å $,$ $v_{n} = 2.18 \times 1 0^{6} \frac{Z}{n}$ m s $^{- 1},$ $E_{n} = - 13.6 \frac{Z ^{2}}{n ^{2}}$ eV
Rydberg
$\overset{ν}{ˉ} = \frac{1}{λ} = R_{H} Z^{2} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}}),$ $R_{H} = 1.097 \times 1 0^{7}$ m $^{- 1}$
Number of lines
$\frac{( n _{2} - n _{1} ) ( n _{2} - n _{1} + 1 )}{2}$

Dual nature and uncertainty

$E = h ν = \frac{h c}{λ};$ $λ = \frac{h}{p} = \frac{h}{m v};$ $Δ x Δ p \geq \frac{h}{4 π}$
Photoelectric effect
$h ν = h ν_{0} + \frac{1}{2} m v^{2}$

Quantum mechanical model

Quantum numbers
$n \geq 1;$ $l = 0 \dots n - 1;$ $m_{l} = - l \dots + l;$ $m_{s} = \pm \frac{1}{2}$
Nodes
radial nodes $= n - l - 1,$ angular nodes $= l,$ total $= n - 1$
Orbital angular momentum
$L = l (l + 1) \frac{h}{2 π}$
Magnetic moment
$μ = n (n + 2)$ BM $(n =$ unpaired electrons $)$
Filling order
$(n + l)$ rule $;$ Aufbau, Pauli, Hund

Some Basic Concepts of Chemistry Classification of Elements and Periodicity in Properties