Atomic Structure: Early Ideas and Dalton's Theory

• Atomic structure is described.

Early Ideas of the Matter

• Democritus: Matter is composed of small cells called atomos.
• Aristotle: Rejected the concept; believed matter is continuous.
• John Dalton: Developed speculations about the atom and applied them to interpret the laws of chemical combination.

Dalton's Atomic Theory

• The atom is the smallest form of all matter.
• Atoms are indivisible, indestructible, and cannot be created.
• All atoms of the same element are the same and different from those of other elements.
• Atoms can combine in definite proportions to form compounds.

Conduction of Electricity Through Gases

• Sir William Crookes studied the effect of pressure on electrical conductivity of gases using a cathode ray tube.
• If a high voltage is applied, electrical current can be passed between two electrodes separated by a gas under reduced pressure.
• At very low pressures (0.25 Nm⁻²) the tube is occupied by a dark space and the glass of tube fluoresces.

Cathode Ray Tube

• A cathode ray tube is used to study electrical discharge in gases.

Goldstein's Study of Dark Space

• Goldstein in 1876 studied the dark space.
• It consists of a stream of particles that originate at the cathode (negative electrode) and move to the anode (positive electrode).
• Particles travel in straight lines in the absence of an external field.
• Particles move in a direction away from the cathode.
• Particles are deflected by both magnetic and electrical fields, indicating a negative charge.

Properties of Cathode Rays

• A paddle wheel placed in the path of cathode rays starts rotating, showing the rays can cause mechanical movement.
• If particles are led into a metal cylinder containing a negative charge, the cylinder becomes negatively charged.
• Particles were named cathode rays by Goldstein because they originate from the cathode.

J.J. Thomson's Experiments

• J.J. Thomson (1897) used the cathode ray tube to measure the velocity and show the charge to mass ratio of the cathode rays.
• Velocity of rays varied with gas in tube, pressure, and potential difference applied.
• Charge to mass ratio had a constant value of 1.7588 x 10¹¹ C kg⁻¹ under all conditions.
• Thomson estimated that the cathode ray particle weighed 1/1000 as much as hydrogen.
• Accurate mass of an electron was obtained by Robert Millikan.
• It suggested that these particles are probably a component of all matter and that atoms contain subatomic particles.
• Atoms must have positively charged species to balance the negative charge of electrons.
• Cathode rays were named electrons by Johnston Stoney.

Discovery of Positive Particles

• In 1886, Goldstein found positively charged particles using a gas discharge tube.
• A high voltage applied to a discharge tube having a perforated cathode and containing air at very low pressure (0.001 mm of mercury) results in a faint red glow observed behind the cathode.
• The red glow arises from rays formed at the anode, and when these rays strike the walls of the discharge tube, they produce faint red light.
• Since these rays are formed at the anode (positive electrode), they are known as anode rays or positive rays.

Properties of Anode Rays

• They travel in straight lines and cast a shadow of the objects placed in their way.
• They produce a mechanical effect: a paddle wheel placed in their path starts rotating.
• Rays are positively charged: Anode rays are deflected towards the negative plate of an electric field.
• The nature of the anode rays depends upon the gas taken in the discharge tube.
• Deflection study of positive particles indicated varying mass. Different gases give different types of positive rays, having different masses and charges.
• Therefore the charge to mass (e/m) ratio is not constant for positive ray particles obtained from different gases.
• Some of the positively charged particles carry a multiple of the fundamental unit of electrical charge.
• The positive particles obtained from hydrogen are the lightest, with a mass 1837 times of electron mass.
• The positive particles obtained from hydrogen gas are called protons from the Greek word 'Proteios', meaning of first importance.

Thomson's Atomic Model

• Evidence for electrons being components of all matter: discovery of radioactivity, identification of β rays as electrons.
• Electrons are given off from a hot metallic wire, which is thermionic emission.
• Electrons are also obtained when light falls on metals (photoelectric effect).
• An atom is made up of a positively charged sphere of low density.
• The positively charged sphere is balanced electrically by negatively charged electrons.

Rutherford's Scattering Experiment

• In 1909 Geiger and Marsden, working in Rutherford's lab, used a beam of α (alpha) particles fired at a very thin sample of gold foil.
• The effect was observed on a fluorescent screen.
• They expected alpha particles to pass through without changing direction.
• The mass was evenly distributed in the atom.
• Positive charges were spread out evenly and were not enough to stop alpha particles.

Interpretation of Deflections in Rutherford's Experiment

• Some alpha particles were deflected or ricocheted.

Rutherford's Conclusions

• The atom has a dense center called the nucleus.
• The nucleus contains the protons and, therefore, has a positive charge.
• The atom is mostly empty space.
• The electrons move around the nucleus as the planets move around the sun.

Classical Theory vs. Rutherford's Atom

• Orbiting electrons are accelerating and should radiate light according to classical theory.
• According to Maxwell's theory, a Rutherford atom would only survive for about 10⁻¹⁷ seconds.

Emission Spectrum of Hydrogen

• Passing an electric current through hydrogen gas at low pressure gives off blue light.
• When this light is passed through a prism, four narrow bands of bright light are observed against a black background.

Spectral Lines and Series

• Apart from lines in the visible region, lines were found in the ultraviolet and infrared regions of the spectrum.
• Many lines could be fitted into series and related to each other in some way.

Named Series

• Lyman: Ultra-violet
• Balmer: Visible
• Paschen: Infra-red
• Brackett: Infra-red
• Pfund: Infra-red

Balmer's Formula

• In 1885, Balmer came up with a simple formula for predicting the wavelength/frequency of any of the lines in the visible region (Balmer series).
• Where R = 1.097 x 10⁷ m⁻¹ and "n" is an integer ≥ 3.

Rydberg's Generalization

• Three years later, Rydberg generalized this so that it was possible to work out the wavelengths of any of the lines in the hydrogen emission spectrum.
• Rydberg equation:
• Rн, is a constant known as the Rydberg constant.
• Rн = 1.09678 x 10⁷ m⁻¹.
• n₁ and n₂ are integers, where n₂> n₁.

Rydberg's Equation in Terms of Frequency

• Rydberg's equation becomes: v/c=RH(1/n₁²-1/n₂²).

Series Limits and Observation Regions

• Lyman: n₁=1, n₂=2,3,4...
• Balmer: n₁=2, n₂=3,4...
• Paschen: n₁=3, n₂=4,5,6...
• Brackett: n₁=4, n₂=5,6,7...
• Pfund: n₁=5, n₂=6,7,8...

Electromagnetic Spectrum

• The region of the electromagnetic spectrum can be determined from the wavelength of the light line that is expected to be observed.

Max Planck's Theory

• Max Planck presented a theoretical explanation of the spectrum of radiation emitted by an object that glows when heated.
• He imagined that the walls of a glowing solid contained a series of resonators that oscillated at different frequencies.
• These resonators gain heat energy from the walls of the object and lose energy in the form of electromagnetic radiation.

Planck's Quantum Theory

• The energy of these oscillators could take on only a limited number of values.
• Because the number of values of the energy of these oscillators is limited, they are theoretically "countable," therefore said to be quantised.
• Energy can be released or absorbed by atoms in discrete chunks or multiples of a minimum size known as a quantum.
• The energy E of a single quantum is given by E = hν, where h is Planck's constant (6.626 x 10⁻³⁴ Js).

Planck's Emission/Absorption Theory

• According to Planck's theory, matter emits or absorbs energy in whole-number multiples of hv. E.g., hv, 2hv, 3hv, etc.
• Albert Einstein extended Planck's work to the light that had been emitted, suggesting light behaved as a stream of small bundles, or packets, of energy which he called photons.
• The energy of a photon is given by E = hν.

Bohr's Model of the Atom

• In 1913, Niels Bohr proposed a model for the hydrogen atom.
• The Bohr model of the atom was based on the planetary model of the atom and provided a theoretical basis for explaining the line spectra of hydrogen atoms.

Bohr's Postulates

• The electron in a hydrogen atom travels around the nucleus in a circular orbit.
• The centripetal force between the electron and nucleus is balanced by the Coulombic attraction between them

Bohr's Postulates Part 2

• Only a limited number of orbits with certain energies are allowed, those for which the angular momentum of the electron is an integral multiple of Planck's constant divided by 2π.
• Where n = orbit number (principal quantum number) and n = 1, 2, 3, 4...

Bohr's Postulates Part 3

• The energy of the electron in an orbit is constant and proportional to its distance from the nucleus, the further the electron is from the nucleus, the more energy it has.

Bohr's Postulate 4

• Electromagnetic radiation is emitted or absorbed if an electron moves from one orbit to another.
• The energy of radiation is equal to the energy difference between the two orbits: ΔE = E₂ - E₁.

Determination of Radius of Hydrogen Atom

• From postulate 1: r = n²h²/4π²me².

First Orbit Radius

• For n=1 (first orbit), r = n²h²/4Μπ² e².
• h = 6.626 x 10⁻²⁴ JS⁻¹, m = 9.1096 X 10⁻³¹ kg, and e = -1.5189 9 X 10⁻¹⁴ kg.
• Radius r = 0.0529 X 10⁻⁹ m = 0.529 Å.
• The radius of the first orbit in the hydrogen atom is called the Bohr radius and denoted by symbol ao.
• The radius of other orbits in hydrogen can be calculated as multiples of using the equation r = n²ao.

Use of Equation 6

• The expression can be used to calculate the radius of any atom once the atomic number is known, or: r = (n²ao)/Z.

Energy of an Orbit

• Combining kinetic and potential energy.

Bohr Orbit Conclusions

• Postulate 3 of Bohr states that each orbit has a definite amount of energy.
• The total energy of an electron is the sum of both kinetic and potential energy.
• E = K + U.
• Kinetic energy, K = ½mv².
• The potential energy, U = -Ze²/r:

Defining the terms

• Equation stating E = ½mv² -Ze²/r

The One Electron Atom

• For the one-electron atom (H, He⁺, Li²⁺, etc.), the lowest energy occurs when n = 1, called the ground state.

Energy Release and Absorbption - Postulate 4

• If the atom receives sufficient energy, its electron jumps to a higher orbit of higher energy, an excited state.
• The atom can assume a lower-energy state through emission of energy in the form of electromagnetic radiation.
• The energy of this radiation is equal to the energy difference between the two states.

Planck's Equation

• Determining frequency with constant values

Wavelength

• An equation that relates the wavelength to the spectrum of hydrogen.

Line Spectrum of Hydrogen

• Bohrs Explanation on how spectral lines correspond to transition states of higher and lower states.

Success of Bohr's Theory

• The Bohr Model was able to explain most features of the hydrogen spectrum.

Shortcomings of Bohr Model

• Failed to get a accurate description of electrons in multi- electron atoms

Revisions to the Model

• Sommerfeld revised parts of Bohr Theory regarding spectral lines and the wave particle theory

Electron Properties

• Electrons can be observed as particles some of the time.

Quantum Mechanics

• Uncertainty and the schroginger equation create equations that give the most accurate values for the location of quantum particles.