The Atom and Quantum Physics

• The atom and the quantum involve the discovery of the atomic nucleus, atomic spectra, Bohr's model of the atom, explanation of quantized energy levels and electron waves

Discovery of the Atomic Nucleus

• Atoms consist mostly of empty space
• Almost all of an atom's mass is located at its center
• Ernest Rutherford demonstrated this space and mass concentration with his gold foil experiment
• The "plum-pudding" model hypothesized evenly distributed mass within an atom

Rutherford's Gold Foil Experiment (1911)

• A beam of positively charged alpha particles was directed through thin gold foil
• Nearly all alpha particles passed through with little or no deflection
• Some particles were deflected from their straight paths
• A few alpha particles were widely deflected; a very small number were scattered backward

Atomic Nucleus Findings

• Most alpha particles went straight through the thin foil
• Some particles were widely deflected
• Some particles were scattered back almost along their incoming path
• There had to be a positively charged object within the atom
• This object had to be very small compared with the size of the atom
• This object had to be massive enough to resist being shoved aside by heavy alpha particles -This resulted in the discovery of the atomic nucleus
• The nucleus occupies less than a trillionth of the volume of an atom
• If bare atomic nuclei could be packed together, it would have a huge density
• Neutron star densities are equivalent to the mass of a Boeing 747 compressed to the size of a small grain of sand

Atomic Spectra: Clues to Atomic Structure

• When atoms are excited, they emit light of certain wavelengths, corresponding to different colors
• The series of colored lines represents the atomic spectra
• Each element produces a unique set of spectral lines
• Hydrogen gas emits a red line, a blue line, and several violet lines
• Spectral lines are like atomic fingerprints
• Rydberg noticed that the sum of the frequencies of two lines often equals the frequency of a third line
• The Ritz combination principle is a general principle building on this observation

Bohr's Planetary Model of the Atom

• The Bohr model states that electron orbits correspond to different energy levels within the atom
• Electrons normally occupy the lowest energy levels available
• Energy levels are quantized, meaning only certain levels are possible
• An electron can be boosted to a higher energy level, such as in gas discharge tubes like neon signs
• When the electron returns to lower levels, light is emitted
• The emitted radiation's frequency is determined by E = hf, where E is the energy difference between the higher and lower energy levels
• The frequency/color depends on the size of the jump
• A bigger jump corresponds to blue light, and a smaller jump corresponds to red light
• The electron's jump from one energy state to another is called a "quantum jump"
• Classical physics says that electrons should continuously emit radiation and spiral into the nucleus
• Electrons emit light ONLY when jumping from a higher to a lower energy level

Strengths of Bohr's Model

• It postponed honeymoon to write up his insights
• He was awarded the Nobel Prize in 1922
• It could explain spectral lines, where the lines correspond to electron transitions between the energy levels of the atoms
• Physicists were able to determine the various energy levels in the atom by examining spectra
• Could explain the formation of X-rays in heavier elements, when electrons jump from outer orbits to innermost orbits, a huge jump, so very high frequency
• Could calculate the ionization energy of hydrogen, or the energy needed to knock an electron out of an atom
• It did not explain why energy levels are quantized
• It needed to think of the electron as a wave

Electron Waves

• Electrons have a wavelength
• Electron orbits exist only when the circumference of the orbit is a whole-number multiple of the wavelength
• Orbits exist only when the wave is in phase and undergoes constructive interence
• An electron is thought of not as a particle located at some point in the atom but as if its mass and charge were spread out into a standing wave surrounding the atomic nucleus with an integral number of wavelengths fitting evenly into the circumferences of the orbits
• De Broglie's theory of matter waves, in 1924, said that every particle has a wave associated with it and the electron wave becomes a standing wave, like one on a musical string
• The electron orbits in an atom have discrete radii because the circumferences of the orbits are whole-number multiples of the electron wavelength
• This results in a discrete energy state for each orbit

Models of the Atom

• Bohr: electrons orbit the nucleus like planets around the sun
• de Broglie: A wave follows along an orbit
• Quantum mechanics: electrons are distributed in a "cloud" throughout the atom's volume, described as a 'cloud of probability'

Quantum Mechanics

• The fundamental equation is Schrödinger's wave equation
• In classical physics, Newton's equation explains how external forces act on objects.
• In quantum physics, Schrödinger's equation explains how matter waves change under the influence of external forces.
• The wave function Ψ represents the possibilities that can occur for a system
• The probability density function gives the probability per unit volume
• Einstein visualized particles of light as concentrated bundles of electromagnetic energy - a quantum
• One quantum of light energy is called a photon
• Matter is quantized by being a whole-number multiple of the mass of a single atom
• Electric charge is quantized by being a multiple of the charge of a single electron
• Energy levels in the atom are quantised – a 'quantum leap'
• Newtonian laws worked well for large objects but not in the microworld of the atom
• The study of motion in the macroworld is called mechanics, or classical mechanics.
• The study of motion in the microworld is called quantum mechanics
• The branch of physics that is the general study of the microworld is called quantum physics

Correspondence Principle

• New theory and old must correspond
• Macroscopic level, classical Newtonian physics
• Microscopic level, quantum physics