SCH4U: History of the Quantum Theory

Transcription

1 SCH4U: History of the Quantum Theory Black Body Radiation When an object is heated, it initially glows red hot and at higher temperatures becomes white hot. This white light must consist of all of the visible colours of light. If this light is measured and a plot of light intensity (brightness) vs wavelength (colour) is observed, a characteristic bell curve results. Max Planck (1899) In 1900, Max Planck proposed that the energy released by hot objects is proportional to the frequency of vibration of their atoms. To explain the "bell curve" Planck propose that energy is "quantized" (ie; noncontinuous) Energy must be absorbed or released in discrete "bundles" that he called "quanta". (ie; particles can only vibrate at defined frequencies which are multiples of some fundamental frequency) The energy of a "quantum" is equal to the vibrational frequency multiplied by a constant (h) (called Planck's constant). E = hf (Planck's constant = h = x10-34 J s) The Dual Nature of Light A) The Double Slit Experiment In 1801, Thomas Young performed the double slit experiment in which monochromatic light is passed through two thin slits and then detected on a detection screen.

2 -2- Young concludes that light is behaving like a wave. When the light waves pass through the slits they spread out like ripples in a pond. When the crests of two waves meet or the troughs of two waves meet, they amplify each other (constructive interference) creating a bright band. When a crest from one wave meets a trough from another, they cancel each other out (destructive interference) creating a dark band. This interaction between the waves results in the constructive and destructive interference pattern observed on the detection screen. B) The Photoelectric Effect (1887) Heinrich Hertz and Philip Lenard observed that electrons are emitted from certain metals as a result of absorbing energy from electromagnetic radiation (ie: light). Electrons emitted in this manner are referred to as photoelectrons and this phenomenon is called the photoelectric effect. Experiment 1: Experiment 2: A metal plate is exposed to red light, no photoelectrons are detected. Increasing the intensity of red light has no effect. The same metal plate is exposed to UV light, photoelectrons are detected. Increasing the intensity of the UV light causes photoelectrons to be detected at a faster rate. Einstein s Explanation of the Photoelectric Effect (1905) Einstein suggested that this effect can only be explained if we assume that light has particle-like properties and travels in quantized packets called photons. The energy of a photon is proportional to the frequency of the light (higher frequency = higher energy). Only photons with some minimum energy are able to knock an electron from the metal plate (ie; UV photons but not red photons). Increasing the intensity of the light increases the number of photons striking the metal plate but not the energy of the photons. Result: photons with the appropriate energy knock electrons from the metal plate. Increasing intensity produces photoelectrons at a faster rate. Regardless of intensity, photons with insufficient energy cannot produce photoelectrons Wave-Particle Duality Some experiments show that light has wave-like properties, other experiments show that it has particle-like properties. This phenomenon is called wave-particle duality which suggests that light is simultaneously both a wave and a particle (or something else that we can t quite visualize). How it appears to us depends on how we chose to look at it.

3 -3- Light and Atomic Spectra A) Dark Line (Absorption) Spectrum White light is passed through a gaseous sample of the element. The light that exits the other side is passed through a prism. What is observed is a series of black lines in the continuous spectrum This pattern of dark lines is specific to the element and is called the dark line or absorption spectrum. The dark line spectrum represents the specific frequencies (colours) of light that have been absorbed by the atoms of the element and are now missing from the visible spectrum. B) Bright Line (Emission) Spectrum A gaseous sample of an element is energized until it begins to emit light. This light is passed through a prism. What is observed is distinct series of light bands of specific colour separated by regions of black. This pattern of coloured lines is specific to each element and is called the bright line or emission spectrum The bright line spectrum with its specific frequencies (colours) represents the only energies of light that the excited atoms of an element can emit. Comparing Dark and Bright Line Spectra The frequencies (energies) of light missing from the dark line spectrum are identical to the frequencies (energies) of light present in the bright line spectrum.

4 -4- Niels Bohr (1913) Bohr saw atomic spectra as evidence that the energy of electrons in an atom is quantized (ie: limited to only certain specific energies). Bohr introduced the first quantum model the atom by concluding that electrons in an atom are confided to discrete energy levels the energies that electrons can possess are determined by the allowable energy levels in the atom In un-energized atoms, electrons would be found in their lowest possible energy levels, known as their ground state. Bohr s Explanation of Atomic Spectra: When energized, electrons can be excited to higher energy levels. Electron promotion requires that the electron gain the exact amount of energy required to make the transition from one allowable level to another. The amount of energy required for a transition is equal to the energy difference between the two levels involved. Bohr concluded that the missing frequencies of light in a dark line spectrum correspond to the specific quanta of energy that will excite an electron from one lower level to another higher level. The frequency of light = the difference in energy ( E) between the two levels Excited electrons will eventually return to lower energy levels by losing energy. This energy is released as a photon of light of a specific frequency (colour). The frequency of light emitted corresponds to the energy difference ( E) between the two energy levels involved in the electron transition. These frequencies of light would be visible as the distinct bands of light in the bright line spectrum. Atomic spectra show these distinct bands of light because electrons cannot exist between energy levels and transitions between levels are instantaneous. To support his theory: Bohr developed a mathematical model of the hydrogen atom based on these ideas He developed an equation that allowed him to determine the energy of an electron in any energy level (n). Knowing the energy of an electron in any energy level allowed Bohr to determine the difference in energy ( E) between any two levels: ΔE = En f En i Using Plank s equation, Bohr was then able to develop an equation that would allow him to predict the frequencies (f) of light that would make up the hydrogen spectrum: ΔE = hf so f = ΔE/h therefore: f = (R H /h)(1/n 2 f 1/n 2 i ) Bohr s model not only successfully predicted the colours of light produced by hydrogen atoms in the visible region (Balmer series) but also those that are produced in the infra-red region (Paschen series) and the ultra-violet region (Lyman series)

5 -5- Louis de Broglie (1923) de Broglie reasoned that if light has both particle and wave properties, then maybe particles also have wave properties. He considered the two equations defining energy: E = hc/ and E = mc 2 By substitution: mc 2 = hc/ Solving for wavelength: = h/mc or = h/mv (where v = speed of particle) Using this equation, de Broglie was able to determine the wavelength of any moving particle given its mass (kg) and speed (m/s). Applying this idea to the atom, de Broglie proposed that an electron behaves like a standing wave bound to the nucleus. To explain the quantized energy of an electron de Broglie proposed that the wavelength of the electron must fit the circumference of its orbit exactly, resulting in only a defined number of allowable electron wavelengths The relationship of an allowed orbit (2 r) and the wavelength ( ) of an electron is given by the equation: 2 r = n (r = radius of orbit, = wavelength and n = integer) The orbit circumference = an integral number of wavelengths (n = 3, n = 4) Werner Heisenberg (1927) Heisenberg (1927) showed that due to the dual nature of matter, it is impossible to know simultaneously with exact precision, the position and momentum of a particle. This became known as the Heisenberg Uncertainty Principle. Heisenberg considered the uncertainty in the measurement of the position of a particle ( q x ) and the uncertainty in the measurement of momentum ( p x ) relative to a defined x axis, he developed the following equation: ( q x )( p x ) h/4 (where h = Planck s constant) The smaller the uncertainty associated with one measurement, the greater the uncertainty of the other eg; q x h/4 p x Applying this to the structure of the atom, it is impossible to know with any degree of certainty where or how an electron moves in an atom. According to Heisenberg s calculations, the uncertainty in the position of an electron in an atom is about the size of the atom itself!

6 -6- Erwin Schrodinger (1926) Schrodinger used conventional wave equations to develop a probabilistic quantum model of the atom. The solutions to this equation provides us with what is called the electron s wave function ( ) which defines the probability of finding an electron in any given location around the nucleus. this region of probability of finding an electron is called an orbital These equations assigned an electron a set of three quantum numbers that defined an electron s energy level, sublevel and orbital. Max Born (1926) Max Born used Schrodinger s equations to develop probability functions that could produce a plot of probability densities which define a 3-dimensional volume in space around the nucleus where there is a 90% probability of finding an electron. This 3-D volume of space in which there is a 90% probability of finding an electron represents the electron s orbital. Wolfgang Pauli (1925) Pauli proposed a fourth quantum number with two possible values to resolve inconsistencies between observed spectra and the developing theory of quantum mechanics. The fourth quantum number relates to a property of the electron called spin which is responsible for an electron s weak magnetic field He formulated the Pauli exclusion principle, which stated that no two electrons could exist in the same quantum state. Paul Dirac (1930) Dirac developed a new version of the wave equation that included the fourth quantum number for electron spin. An electron can have one of two possible spins; up or down, resulting in two opposing magnetic fields. Electrons with opposite spin would have opposite magnetic fields which would minimize repulsion forces allowing these electrons to share the same region in space (orbital). Result: two spin paired electrons can occupy the same orbital.