Atoms

 

 

Atoms are the building blocks of matter, with a complex structure that dictates the chemical and physical properties of elements. Understanding atomic theory and structure is essential for further studies in chemistry and physics.

Introduction

Historical Evidence: By the nineteenth century, substantial evidence supported the atomic hypothesis of matter.
 

Discovery of Electrons: 
   - In 1897, J. J. Thomson's experiments with electric discharge through gases revealed that atoms contain negatively charged electrons, which are identical across different elements.
   - Atoms are electrically neutral.
   - A key question arises regarding the arrangement of positive charge and electrons within the atom.

Plum Pudding Model: 
   - In 1898, J. J. Thomson proposed the first atomic model, stating positive charge is uniformly distributed with electrons embedded within, likened to seeds in a watermelon.
   - Subsequent research disproved this model.

Emission of Electromagnetic Radiation: 
   - Condensed matter and dense gases emit radiation with a continuous spectrum, indicative of atomic oscillations governed by inter-atomic interactions.
   - Conversely, rarified gases emit discrete wavelengths, forming a spectrum of bright lines.

Characterization of Elements: 
   - Each element has a characteristic emission spectrum; for example, hydrogen produces a specific set of spectral lines.

Balmer's Formula: 
   - In 1885, Johann Jakob Balmer derived an empirical formula explaining the wavelengths of certain lines emitted by hydrogen.

 

Rutherford’s Nuclear Model: 

    - Ernst Rutherford's 1906 experiments on α-particles led to the investigation of atomic structure. 
   - This model posits that positive charge and most mass are concentrated in a small nucleus, with electrons orbiting around it like planets around the sun.
   - The model was significant but failed to explain the emission of light in discrete wavelengths.

Limitations of Classical Model: 
    - The classical picture, likening electron orbits to planetary orbits, faces challenges in explaining the complexities of atomic spectra, particularly in simple atoms like hydrogen.

 

An atom consists of:

• Nucleus:
  • Contains protons (positively charged) and neutrons (neutral).
  • Center of the atom; occupies a small space but contains most of the mass.
• Electrons:
  • Negatively charged particles that orbit the nucleus in various energy levels (shells).
  • The arrangement of electrons determines the chemical properties of the element.

Atomic Number and Mass Number

• Atomic Number (Z): Number of protons in the nucleus. It defines the element.
• Mass Number (A): Total number of protons and neutrons in the nucleus. 

 

Models of the Atom

Atom models

Dalton's Atomic Model

• Proposed that atoms are indivisible particles that combine in fixed ratios to form compounds.
• Did not explain the structure of the atom.

Thomson's Model (Plum Pudding Model)

• Suggested that atoms are uniform spheres of positively charged matter with negatively charged electrons embedded within, like "plums in a pudding."

Rutherford's Model

• Introduced the concept of a dense, positively charged nucleus.
• Conducted the gold foil experiment, revealing that most of an atom's mass is concentrated in the nucleus.

Bohr's Model

• Proposed that electrons move in defined orbits around the nucleus.

• Introduced the idea of quantized energy levels, explaining electron transitions and the emission of light.

Quantum Mechanical Model of the Atom

• Based on Schrödinger's wave equation.
• Electrons exist in probability clouds (orbitals) rather than fixed paths.
• The model accounts for electron arrangements based on quantum numbers.

Quantum Numbers

• Principal Quantum Number (n): Indicates the energy level.
• Azimuthal Quantum Number (l): Indicates the subshell (s, p, d, f).
• Magnetic Quantum Number (m): Indicates the orientation of orbitals.
• Spin Quantum Number (s): Indicates the spin of the electron.

Periodic Trends

• Atomic Radius: Decreases across a period and increases down a group.
• Ionization Energy: Energy required to remove an electron; increases across a period and decreases down a group.
• Electronegativity: Tendency of an atom to attract electrons; increases across a period and decreases down a group.

Rutherford's Alpha Scattering Experiment

The alpha scattering experiment conducted by Ernest Rutherford, Hans Geiger, and Ernest Marsden in 1911 is fundamental in the field of atomic physics. It leaded to establishment of Atomic Structure through:

• Nuclear Model Confirmation: The experiment provided clear evidence supporting the nuclear model of the atom, where a small, dense nucleus contains most of the atom's mass and positive charge.
• Deflection Observation: Some alpha particles were deflected at large angles, indicating that the nucleus must have a significant positive charge to cause such deflections.  

2. Experiment Design

• Directed a narrow beam of 5.5 MeV alpha-particles from a {214}_{83}Bi radioactive source at a thin gold foil.
• The gold foil had a thickness of 2.1 x 10^{-7} m.
• The scattered alpha-particles were observed using:
• A zinc sulphide screen.
• A microscope to view scintillations (light flashes) produced by strikes on the screen.

3. Observation and Data Collection

• Scattering Pattern: Graphs plotted the number of alpha-particles scattered at different angles.
• Most alpha-particles passed through without collisions.
• Only 0.14% scattered by more than 1°.
• About 1 in 8000 deflected by more than 90°.

4. Conclusions Drawn

   - A large repulsive force is needed to deflect an alpha-particle significantly.
   - Suggests that most mass and positive charge of the atom is concentrated at the center. Rutherford is credited with discovering the nucleus.
 

Rutherford's Nuclear Model of the Atom

1. Structure of the Atom
   - The nucleus contains all positive charge and most of the mass.
   - Electrons orbit the nucleus, similar to planets orbiting the sun.

2. Size Estimates
   - Size of the nucleus: 10^{-15} m to 10^{-14} m.
   - Size of the entire atom: 10^{-10} m.
     - The atom is approximately 10,000 to 100,000 times larger than the nucleus.

3. Implications of Model
   - Most of an atom is empty space.
   - This explains why most alpha-particles go through thin metal foils.
   - When alpha-particles come close to the nucleus, they experience significant scattering due to the strong electric field.
 

The Rutherford Model

1. Central Nucleus and Electron Orbits:

   • The atom is structured similarly to a solar system, with a central nucleus and electrons revolving around it.

2. Forces at Play:

   • The planetary system is held together by gravitational forces, while the interaction in an atom is governed by Coulomb’s Law, as the nucleus and electrons are charged.

3. Acceleration of Electrons:

   • An electron moving in a circular orbit is centripetally accelerated.
   • According to classical electromagnetic theory, an accelerating charged particle emits electromagnetic radiation, leading to energy loss.

4. Stability Issues:

   • As the electron loses energy, it should spiral inward and eventually collide with the nucleus, rendering the atom unstable.

5. Emission of Continuous Spectrum:

   
   Classical theory predicts that the frequency of emitted light corresponds to the electron's revolution. As the electron spirals inward, both its angular velocity and frequencies change, leading to a continuous spectrum, contrasting with the line spectrum observed experimentally.

The Line Spectra of the Hydrogen Atom

Introduction to Line Spectra

The line spectra of the hydrogen atom consist of distinct lines corresponding to specific wavelengths of light emitted or absorbed by the hydrogen atom. These lines arise from transitions between the quantized energy levels of the atom, illustrating the discrete nature of atomic energy states.

Origin of Line Spectra

1. • Hydrogen atoms have specific energy levels defined by the principal quantum number $n$. The energy levels are given by the formula: $E_n=-\frac{13.6\text{eV}}{n^2}$
   • Here, $n$ can take positive integer values (1, 2, 3, ...).
2. • When an electron transitions from a higher energy state $n_i$ to a lower energy state $n_f$, a photon is emitted with energy corresponding to the difference in energy levels: $h\nu =E_{n_i}-E_{n_f}$
   • This results in spectral lines at specific frequencies or wavelengths.

Spectral Series of Hydrogen

The hydrogen line spectra are categorized into several series based on transitions to or from the respective energy levels:

1. Lyman Series:

   • Transitions from $n\ge 2$ to $n=1$.
   • Ultraviolet region of the spectrum.
   • Wavelengths: $\approx 121.6\text{nm}$ (Fifth line), $\approx 102.6\text{nm}$, etc.

2. Balmer Series:

   • Transitions from $n\ge 3$ to $n=2$.
   • Visible region of the spectrum.
   • Wavelengths: $656.3\text{nm}$ (red), $486.1\text{nm}$ (blue-green), $434.0\text{nm}$ (blue-violet), etc.

3. Paschen Series:

   • Transitions from $n\ge 4$ to $n=3$.
   • Infrared region of the spectrum.
   • Wavelengths: $1875\text{nm}$, $1281\text{nm}$, etc.

4. Brackett Series:

   • Transitions from $n\ge 5$ to $n=4$.
   • Infrared region of the spectrum.

5. Pfund Series:

   • Transitions from $n\ge 6$ to $n=5$.
   • Infrared region of the spectrum.

 Bohr's Modifications

1. • Niels Bohr recognized that classical theories failed to adequately describe atomic phenomena and he introduced Quantum Concepts:

     Bohr's Postulates:

     • First Postulate: An electron can exist in certain stable orbits without emitting energy, defining stationary states.
     • Second Postulate: The angular momentum of electrons in stable orbits is quantized, given by the equation $L=\frac{nh}{2\pi }$ (where $h$ is Planck’s constant).
     • Third Postulate: Electrons can transition between energy levels, emitting or absorbing photons with energy equal to the difference in energy states, expressed as: $h\nu =E_i-E_f$
     
     

     Energy Levels:

     • The lowest energy state (ground state) for hydrogen has an energy of -13.6 eV, and energy levels become less negative as n increases.
     • The minimum energy required to ionize the electron from the ground state is 13.6 eV. 

   Energy Levels and States of the Hydrogen Atom

   Ground State and Energy Levels

   1. Ground State:

      • The lowest energy state of the hydrogen atom occurs when the electron is in the orbit closest to the nucleus, defined by the principal quantum number n = 1.
      • The energy of this ground state (E1) is –13.6 eV. This negative value indicates that energy must be added to the electron to free it from the atom.

   2. Ionization Energy:

      • The minimum energy required to ionize the hydrogen atom, transitioning the electron from the ground state to being free, is 13.6 eV.

   3. Excited States:

      • As the quantum number n increases (n = 2, 3, ...), the energy levels of the atom become less negative:
        • For n = 2, the energy (E2) is –3.40 eV.
        • For n = 3, the energy (E3) is –1.51 eV.
      • The energy required to excite the electron from one state to another can be calculated as the difference between energy levels.

   Energy Change Calculations

   • To determine the energy needed to excite the atom:
     • From E2 to E1: $\Delta E=E2-E1=-3.40\text{eV}-(-13.6\text{eV})=10.2\text{eV}$
     • From E3 to E1: $\Delta E=E3-E1=-1.51\text{eV}-(-13.6\text{eV})=12.09\text{eV}$

   Photon Emission

   • When an electron transitions from a higher energy state to a lower one, it emits a photon. The energy of the emitted photon corresponds to the energy difference between the two states: $E_{photon}=E_{initial}-E_{final}$

   Energy Level Diagram

   • The energy level diagram illustrates how the energy states become progressively less negative as n increases.
   • The maximum energy state (0 eV) occurs when the electron is completely removed from the nucleus (at infinite distance).
   • The energies of excited states converge as n increases, indicating that the differences in energy become smaller.

    

    

   Bohr's Model: Photon Emission and Absorption

   Third Postulate of Bohr’s Model

   1. Energy Transition:

      • When an atom transitions from a higher energy state (quantum number $n_i$) to a lower energy state (quantum number $n_f$), energy is released in the form of a photon.
      • The energy difference is given by:
        $h{\nu }_{if}=E_{n_i}-E_{n_f}$
      • Here, ${\nu }_{if}$ represents the frequency of the emitted photon, and $h$ is Planck's constant.

   2. Discrete Frequencies:

      • Since both $n_f$ and $n_i$ are integers, this leads to the conclusion that transitions produce light at discrete frequencies, resulting in quantized energy levels.

   Spectral Lines

   1. Emission Lines:

      • When an electron jumps from a higher energy state to a lower one, a photon is emitted, producing an emission line in the atomic spectrum.

   2. Absorption Process:

      • Conversely, if an atom absorbs a photon of precisely the right energy to promote an electron from a lower energy state to a higher one, this process is called absorption.
      • If photons with a continuous range of frequencies pass through a rarefied gas, a spectrometer will reveal dark spectral absorption lines in the continuous spectrum.
      • These dark lines indicate the specific frequencies absorbed by the gas atoms, corresponding to the energy differences between levels.

   Significance of Bohr’s Model

   • Bohr’s model provided a successful explanation for the observed spectrum of hydrogen, predicting the wavelengths of spectral lines and establishing a foundation for understanding atomic structure.
   • The model's insights into discrete energy levels and photon interactions stimulated significant advancements in quantum theory and atomic physics.

   Recognition

   • In 1922, Niels Bohr was awarded the Nobel Prize in Physics for his groundbreaking work on the hydrogen atom and his contributions to quantum theory, recognizing the profound impact of his model on modern physics.