Study sheet: Atomic Structure and Bohr Model

📋 Course Outline

1. Dalton’s Atomic Theory
2. Discovery of Subatomic Particles
3. Atomic Numbers and Isotopes
4. Atomic Mass and Isotopic Abundance
5. Electromagnetic Radiation
6. Planck’s Quantum Theory
7. Photoelectric Effect
8. Limits of Rutherford’s Model
9. Bohr’s Atomic Model
10. Hydrogen Spectra and Bohr Limits

📖 1. Dalton’s Atomic Theory

🔑 Key Concepts & Definitions

• Dalton’s atomic theory : Dalton’s atomic theory — proposed by John Dalton in 1808, regarded the atom as the indivisible ultimate particle of matter

📝 Essential Points

• The theory explained these laws:
  • conservation of mass
  • constant composition
  • multiple proportions

📖 2. Discovery of Subatomic Particles

🔑 Key Concepts & Definitions

• Electron : a negatively charged subatomic particle found in all atoms and identified through cathode-ray experiments
• Nucleus : the tiny, dense, positively charged region of an atom that contains almost all of its mass

★ Must-know

• The experiment showed that cathode rays: travel from cathode to anode, travel in straight lines without electric or magnetic fields, produce fluorescence on zinc sulfide screens

• Millikan’s oil-drop experiment measured the electron charge as approximately $-1.6\times10^{-19}\ \mathrm{C}$, with the accepted value given as $-1.602176\times10^{-19}\ \mathrm{C}$. — R.A. Millikan, oil drop experiment

• Chadwick discovered the neutron in 1932 by bombarding beryllium with alpha particles; the neutron is neutral and has approximately the same mass as the proton. — James Chadwick

Further detail

📐 Formula — Thomson determined the electron charge-to-mass ratio as $\frac{e}{m_e}=1.758820\times10^{11}\ \mathrm{C\,kg^{-1}}$, with the electron charge being negative. — J.J.Thomson, 1897

💡 Memory Hook

Electron → proton/nucleus → neutron

📖 3. Atomic Numbers and Isotopes

🔑 Key Concepts & Definitions

• Atomic number : the number of protons in an atom’s nucleus and equals the number of electrons in a neutral atom
• Mass number : the total number of protons and neutrons, or nucleons, in an atom’s nucleus
• Isotopes : atoms of the same element that have the same number of protons but different numbers of neutrons and therefore different masses
• Atomic mass unit : The atomic mass unit, u, is defined as one-twelfth of the mass of a carbon-12 atom and has the value $1\,\mathrm{u}=1.660539\times10^{-27}\,\mathrm{kg}$.

💡 Memory Hook

Atomic number identifies the element; mass number counts nucleons

📖 4. Atomic Mass and Isotopic Abundance

★ Must-know

📐 Formula — The weighted average atomic mass is calculated by $\overline{M}=F_1M_1+F_2M_2+\cdots+F_nM_n$, where each fraction isotope abundance is $F_i=\frac{\text{abundance percentage}}{100}$.

Further detail

• For silver, the isotope masses 106.90509 u and 108.90470 u with abundances 51.89% and 48.14% give an average atomic mass of 107.867 u.

📖 5. Electromagnetic Radiation

🔑 Key Concepts & Definitions

• Electromagnetic wave : James Clerck Maxwell — consists of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation

★ Must-know

📐 Formula — The speed of electromagnetic radiation is related to wavelength and frequency by $c=\lambda\nu$.

Further detail

• Wavelength is measured in metres, with common submultiples including micrometres $10^{-6}\,\mathrm{m}$ and nanometres $10^{-9}\,\mathrm{m}$, while frequency is measured in hertz.

💡 Memory Hook

Perpendicular electric and magnetic fields moving together through space

📖 6. Planck’s Quantum Theory

🔑 Key Concepts & Definitions

• Planck’s quantum theory : Planck — states that electromagnetic radiation is emitted or absorbed in discrete energy units called quanta rather than as a continuous flow

📝 Essential Points

📐 Formula — The energy of radiation is given by $E=nh\nu=\frac{nhc}{\lambda}$, where $h=6.626\times10^{-34}\,\mathrm{J\,s}$ and $n$ is an integer. — Planck

💡 Memory Hook

Continuous classical energy versus quantized energy packets

📖 7. Photoelectric Effect

🔑 Key Concepts & Definitions

• Photoelectric effect : Einstein, PHOTOELECTRIC EFFECT — the emission of electrons from a metal surface when incident radiation has sufficient energy and frequency

📝 Essential Points

📐 Formula — For photoemission, the photon energy satisfies $E=W_{\mathrm{extr}}+E_c=E_0+E_c$, with $E=h\nu$ and $E_c=\frac{1}{2}mv^2$. — Einstein, PHOTOELECTRIC EFFECT

📌 The photoelectric effect occurs only when the incident frequency exceeds the threshold frequency, so $\nu>\nu_0$ and equivalently $\lambda<\lambda_0$.

💡 Memory Hook

Sufficient photon frequency → electron emission

📖 8. Limits of Rutherford’s Model

★ Must-know

📌 Rutherford’s model cannot explain atomic stability because an orbiting electron should continuously radiate energy, spiral toward the nucleus, and eventually fall into it.

📌 Rutherford’s model predicts continuous spectra from continuous energy loss, whereas observed atomic spectra contain discrete lines of definite frequencies.

Further detail

• Hydrogen emission spectra are obtained when excited hydrogen gas emits light that is separated by a prism into isolated sharp lines.

💡 Memory Hook

Continuous radiation loss → collapsing electron and unstable atom

📖 9. Bohr’s Atomic Model

📝 Essential Points

📌 Bohr proposed that electrons occupy only permitted circular orbits in which their energy remains constant, called stationary states.

📌 According to Bohr’s energy postulate, an electron absorbs or emits energy when it changes from one allowed orbit or energy level to another.

📐 Formula — The Bohr radius of the hydrogen atom is $r_n=0.53n^2\,\mathrm{\AA}$ for $n=1{,}2{,}3,\ldots$, with $r_1=0.53\,\mathrm{\AA}=0.529\times10^{-10}\,\mathrm{m}$. — Niels Bohr, BOHR’S ATOMIC MODEL

📐 Formula — The energy of a hydrogen electron in level $n$ is $E_n=-\frac{13.6}{n^2}\,\mathrm{eV}$, and the ground-state energy is $E_1=-13.6\,\mathrm{eV}=-2.18\times10^{-18}\,\mathrm{J}$.

💡 Memory Hook

Allowed orbit → energy change → photon emission or absorption

📖 10. Hydrogen Spectra and Bohr Limits

★ Must-know

• Hydrogen emission occurs when an electron drops from a higher energy level to a lower level and emits a photon whose energy equals the difference between the two levels.

• The hydrogen spectral series are:

  • Lyman — ultraviolet
  • Balmer — visible
  • Paschen — infrared
  • Brackett — infrared
  • Pfund — infrared
  • Humphrey — far-infrared

📐 Formula — The Balmer–Rydberg relation is $\frac{1}{\lambda}=R_H\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$, where $R_H=1.09677\times10^7\,\mathrm{m^{-1}}$. — Johann Balmer and Johannes Rydberg

• The model fails to explain:
  • multi-electron spectra
  • hydrogen fine structure
  • Zeeman splitting
  • Stark splitting
  • Heisenberg’s uncertainty principle

Further detail

• The ionization energy of hydrogen is the energy required to move an electron from the ground state to infinity and equals 13.6 eV or 2.17 × 10−18 J.

📐 Formula — For a hydrogen-like ion with nuclear charge $Z$ and one electron, the Bohr energy is $E_n=-\frac{13.6Z^2}{n^2}\,\mathrm{eV}$ and the orbit radius is $r_n=\frac{n^2}{Z}r_1$.

💡 Memory Hook

Hydrogen-like success versus multi-electron and fine-spectrum limitations

📊 Synthesis Tables

Fundamental Subatomic Particles

Particle	Charge	Location or role
Electron	Negative	Located around the nucleus
Proton	Positive	Located in the nucleus
Neutron	Neutral	Located in the nucleus; approximately the mass of a proton