Atomic Structure Essentials

This cheat sheet summarizes key formulas, constants, and concepts related to atomic structure, covering sub-atomic particles, nuclear properties, quantum theory, and atomic models.

Core Principles

Atomic radius is ~10^-10 m; nuclear radius is ~10^-15 m.
Neutron is the heaviest sub-atomic particle; electron is the lightest.
Photon energy is directly proportional to frequency (E=hν).
Photoelectron KE depends on light frequency, not intensity.
Bohr model quantizes electron orbits and energy levels.
Rydberg formula predicts spectral lines for hydrogen-like atoms.
de Broglie wavelength describes the wave nature of matter.
Heisenberg's principle limits simultaneous precision of position and momentum.

Action Steps

Calculate specific charge for different particles.
Determine nuclear radius using mass number.
Apply Planck's equation to find energy of photons.
Analyze photoelectric effect data to find work function.
Use Bohr model formulas for hydrogen-like atoms.
Apply Rydberg formula to predict spectral lines.
Calculate de Broglie wavelength for moving particles.
Assess uncertainty limits using Heisenberg's principle.

Formulas

Specific Charge (electron): $\frac{e}{m_e} = 1.758820 \times 10^{11} \text{ C/kg}$
Electron Charge: $e = -1.6 \times 10^{-19} \text{ C}$
Electron Mass: $m_e = 9.1 \times 10^{-31} \text{ kg}$
Proton Mass: $m_p \approx 1.672 \times 10^{-27} \text{ kg}$
Neutron Mass: $m_n \approx 1.675 \times 10^{-27} \text{ kg}$
Nuclear Radius: $R = R_0 (A)^{1/3}$
Distance of Closest Approach: $r = \frac{4KZe^2}{m_{\alpha}v_{\alpha}^2}$
Wave Speed: $\nu = \frac{c}{\lambda}$
Planck's Equation: $E = h\nu = \frac{hc}{\lambda}$
Energy Shortcut: $E(\text{eV}) = \frac{12400}{\lambda(\text{\AA})}$
Photoelectric Effect: $h\nu = \phi + K.E.$
Work Function: $\phi = h\nu_0 = \frac{hc}{\lambda_0}$
Bohr Angular Momentum: $mvr = \frac{nh}{2\pi} = n\hbar$
Bohr Orbit Radius: $r_n = 0.529 \times \frac{n^2}{Z} \text{ \AA}$
Bohr Electron Velocity: $v = 2.18 \times 10^6 \times \frac{Z}{n} \text{ m/s}$
Bohr Total Energy: $E_n = -13.6 \times \frac{Z^2}{n^2} \text{ eV/atom}$
Rydberg Formula: $\bar{\nu} = \frac{1}{\lambda} = R_H \cdot Z^2 \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} \right]$
de Broglie Wavelength: $\lambda = \frac{h}{mv} = \frac{h}{\sqrt{2mK.E.}}$
Heisenberg Uncertainty: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$

Key Terms

Specific Charge: Ratio of electric charge to mass (e/m).
Work Function ($\phi$): Minimum energy required to remove an electron from a metal surface.
Quantization: The concept that physical quantities can only have discrete values.
Mass Number (A): Total number of protons and neutrons in an atomic nucleus.
Photoelectric Effect: Emission of electrons from a material when light shines on it.
de Broglie Wavelength: Wavelength associated with a moving particle, reflecting its wave-like nature.
Uncertainty Principle: Fundamental limit to the precision with which certain pairs of physical properties can be known simultaneously.

Timeline

Early 20th Century: Development of Quantum Theory (Planck).
1911: Rutherford proposes the nuclear model of the atom.
1913: Bohr proposes his atomic model for hydrogen.
1905: Einstein explains the photoelectric effect using quantum theory.
1924: de Broglie proposes the wave nature of matter.
1927: Heisenberg formulates the uncertainty principle.

People

J.J. Thomson: Discovered the electron and determined its charge-to-mass ratio.
Robert Millikan: Determined the elementary charge of an electron.
Ernest Rutherford: Developed the nuclear model of the atom based on scattering experiments.
Max Planck: Introduced quantum theory, proposing energy is quantized.
Albert Einstein: Explained the photoelectric effect and proposed mass-energy equivalence.
Niels Bohr: Developed the Bohr model of the atom, incorporating quantum ideas.
Louis de Broglie: Proposed that matter exhibits wave-like properties.
Werner Heisenberg: Formulated the uncertainty principle.