Basic Knowledge to Build the Quantum Theory

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1. I. Scientists have accepted the notion of atoms even prior to the time of Dalton who developed a crude atomic theory based upon the work of Lavosier, Proust and himself.
• Lavosier: Law of Conservation of Mass
• Proust: Law of Definite Proportions
• Dalton: Law of Multiple proportions
From that time, scientists (chemists and physicists) have been concerned with the nature of the atom.
• Dalton: "billiard ball" or "bb" model
• Thompson: "plumb pudding" or "raisin bun" model
• Rutherford: "nucleus model" with electrons orbiting the nucleus
The development in physics during the first thirty years of the 20th century led to a greater understanding of the nature of the atom, particularly the organization of the electron cloud (the mostly empty space around the nucleus from Rutherford).

The tool that was used to "dissect" or probe the atom was electromagnetic radiation (EMR), form of energy thought (remember our time frame in history) to consist entirely of waves oscillating in electric and magnetic force fields positioned at right angles with respect to each other.

To understand EMR, terms associated with wave motion must be defined and understood.

wavelength (lambda, ), the distance between two adjacent points that are "in phase."  , measured in length units: m, cm, nm, å ...
1 nm = 1x10-9 m, 1 angstrom (å) = 1x10-10 m, 1 nm = 10 å

frequency ( f or v ), the number of waves passing a given fixed point per unit time.

• measured in waves per sec, cycles per sec (cps), vibrations per sec
• SI unit is hertz (Hz) defined as or s-1
• mathematically, frequency is always used as velocity (v or c, for all forms of EMR), the distance traveled by a fixed point on a wave per unit time.

• measured in velocity units of km/s or m/s
• for all forms of EMR, c is a constant in a vacuum @ 2.9979x108 m/s or 2.9979x105 km/s

Putting wavelength, frequency, and velocity together
(m) x ( ) = m/s v = c = wavelength in m
v = frequency in c = speed of light

Since c is a constant, v & are inversely proportional

• as v increases the decreases: high v, short • as v decreases the increases: low v, long  2. The Nature of Matter
At the end of the nineteenth century, the idea prevailed that matter and energy were distinct. Matter was thought to consist of particles, while energy in the form of light was described as a wave. The assumption was that there was no intermingling of matter and light.

Max Planck (1901) was studying radiation emitted by solid bodies heated to incandescence. Planck found that his results could not be explained in terms of current nineteenth century physics. Planck discovered that energy can only be gained or lost in integer multiples (n) of h v, h is called Planck's constant (6.626x10-34 J s) and v the frequency. E = nh v E = Energy of quanta
n = integer
h = Planck's constant
v = frequency of EMR

Planck's results showed that energy was quantized. Planck called each of the small "packets" of energy a quantum (singular, noun). Energy can only be transferred in whole quanta, therefore energy seems to have particulate properties.

Albert Einstein (1905) showed that electromagnetic radiation is quantized. Electromagnetic radiation can be viewed as a stream of "particles", Planck called these particles quanta, Einstein called the stream of "particles" photons (the term photon was "coined" by G.N. Lewis)

Ephoton = hv = The energy of the photon found from the above equation could be then plugged into Einstein's famous equation E = mc2. Solve for m and obtain:
m = Einstein had theoretically proven that a photon of light has mass or mass energy. American physicist Arthur Compton performed experiments in 1922 proving Einstein's relationship above. This was the beginning of physics for the twentieth century. The new physics was later called quantum physics.

Summary of Planck and Einstein's work

1. Energy is quantized. It can occur only in discrete units called quanta.
2. Electromagnetic radiation, which was previously thought to exhibit only wave properties, seems to show certain characteristics of particulate matter as well. This phenomenon is sometimes referred to as the Wave Particle Duality of Nature.

3. Atomic Spectrum of Hydrogen
The excited hydrogen electron produces a line spectrum from the photons when examined through a spectroscope (instrument that breaks up light by diffraction). This shows that only certain energies are allowed for the electron in the hydrogen atom. In other words, the energy of the electron is quantized. Changes in energy between energy levels in hydrogen will produce only certain wavelengths of emitted light. For hydrogen = 410 nm, 434 nm, 486 nm, 656 nm.