CHEMCA
EXAM MASTER FORMULA SHEET
Structure of Atom
High-Yield Content for JEE Main, Advanced & NEET
h (Planck's): \(6.626 \times 10^{-34} \text{ J s}\)
c (Speed of light): \(3 \times 10^{8} \text{ m/s}\)
Mass of \(e^-\): \(9.1 \times 10^{-31} \text{ kg}\)
1 eV: \(1.6 \times 10^{-19} \text{ J}\)
1. Electromagnetic Radiation & Dual Nature
Planck's Quantum Theory:
\[ E = h\nu = \frac{hc}{\lambda} \]
Shortcut: \(E (\text{eV}) \approx \frac{12400}{\lambda (\text{\AA})}\)
Photoelectric Effect:
\[ h\nu = \phi + K.E._{max} \implies h\nu = h\nu_0 + \frac{1}{2}mv^2 \]
\(\phi\) = Work Function, \(\nu_0\) = Threshold Frequency
2. Bohr's Atomic Model (Single-species)
Applicable for \(H, He^+, Li^{2+}, \dots\)
Radius of \(n^{th}\) orbit:
\[ r_n = 0.529 \times \frac{n^2}{Z} \text{ \AA} \]
Velocity of \(e^-\):
\[ v_n = 2.18 \times 10^6 \times \frac{Z}{n} \text{ m/s} \]
Energy of \(n^{th}\) orbit:
\[ E_n = -13.6 \times \frac{Z^2}{n^2} \text{ eV/atom} \]
\(P.E. = 2 \times E_n\)
\(K.E. = -E_n\)
3. Hydrogen Spectrum
Rydberg Formula:
\[ \frac{1}{\lambda} = \bar{\nu} = R_H Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
\(R_H \approx 1.097 \times 10^7 \text{ m}^{-1}\)
Total Spectral Lines (Sample):
\[ \frac{(n_2 - n_1)(n_2 - n_1 + 1)}{2} \]
- Lyman: \(n_1=1\) (UV)
- Balmer: \(n_1=2\) (Visible)
- Paschen: \(n_1=3\) (Infrared)
4. Quantum Mechanical Model
de-Broglie Wavelength:
\[ \lambda = \frac{h}{mv} = \frac{h}{\sqrt{2mK.E.}} \]
Heisenberg Uncertainty:
\[ \Delta x \cdot \Delta p \ge \frac{h}{4\pi} \]
Nodes Calculation:
Radial Nodes
\(n - l - 1\)
Angular Nodes
\(l\)
Total Nodes
\(n - 1\)
5. Quantum Numbers & Shells
| Quantum Number | Symbol | Range / Value |
|---|---|---|
| Principal | \(n\) | \(1, 2, 3 \dots\) (Size/Energy) |
| Azimuthal | \(l\) | \(0\) to \((n-1)\) (Shape) |
| Magnetic | \(m_l\) | \(-l\) to \(+l\) (Orientation) |
| Spin | \(s\) | \(+1/2, -1/2\) |
Max electrons in shell: \(2n^2\) | Max electrons in orbital: \(2\)
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