Objective 6: TSW explain how the quantum mechanical model evolved from Bohr’s model.

Bohr’s model worked well only for hydrogen or any atom with a single electron Two things had to happen before the quantum mechanical model was developed Development of quantum mechanics Realization of the dual nature of matter

Max Planck developed quantum mechanics in 1900 He was studying how objects radiate energy (heat) He discovered that the heat was being given off in bursts of energy which are called quanta

Classical vs. Quantum Mechanics Classical mechanics viewed energy transfer as continuous When you drop an object from a height, the potential energy it had at the height is continuously transferred to kinetic energy as it falls and gains speed Quantum mechanics views energy transfer as quantized The object at the height is in an energy state and when you “drop” it, that energy is given off all at once and moves to a lower energy state

Dual Nature of Matter Light has a dual nature, it has characteristics of waves and of particle Wave characteristics include having a wavelength (λ) and a frequency (f) and thus v = λf Waves can also form interference patterns in which the amplitude of height of the wave is increased (constructive interference) or decreased (destructive interference) as the waves pass through each other

Light produces interference patterns when light shines through diffraction gratings White light produces a rainbow effect Monochromatic light (light of a single frequency) produces alternating areas of light and dark Technologies which take advantage of the wave nature of light: laser-based surveying, holograms, check-out-scanners, CDs and DVDs

Particle characteristics of light include the ability to reflect off of surfaces and that it has a speed Photoelectric effect: the ejection of electrons from a metal surface when that surface is exposed to electromagnetic radiation of sufficiently high frequency In 1905 Einstein was able to explain the photoelectric effect by using Planck’s quantum theory (for which he won the Nobel prize in 1921)

If light is being given off in bursts as Planck suggested in quantum mechanics, it is a stream of particles (photons) each with a specific amount of energy, E = hf If the photon has sufficient energy to knock an electron out of an atom, then it will be ejected, if it isn’t of high enough energy nothing will happen Technologies which take advantage of the particle nature of light: photography, photocopying machines, photodiode technologies

Just to clarify, light has a dual nature but it does not and cannot exhibit both characteristics at the same time: if you treat it like a wave, it will behave like a wave and if you treat it like a particle, it will behave like a particle In the 1920s, Louis de Broglie asked (and answered) if light could behave both as a wave and a particle, could particles such as electrons demonstrate wave behaviors

He connected demonstrated mathematically that it was possible for a particle to have a wavelength de Broglie’s equation an equation which defines the wavelength of a particle, λ = h/mv E = mc 2 E = hf mc 2 = hf c is no longer the speed of light but the speed of a particle and since the wave equation rearranged is f = v/λ mv 2 = hv/λ and rearranging and cancelling leads to de Broglie’s equation: λ = h/mv

The significance of the de Broglie equation is that it demonstrates that particles have wave behaviors If you are dealing with an electron moving at speeds near the speed of light you find it has a sufficiently large wavelength so that its wavelength is close to that of ordinary electromagnetic radiation In the late 1920s, scientists observed electron diffraction patterns thus confirming de Broglie’s mathematics

Quantum Mechanical Model of the Atom In 1926, Erwin Schrödinger announced a new model of the atom based on quantum mechanics and probability He treated the electron not as a particle, but as a wave Max Born added to the concept by saying that since the electron was being treated as a wave, its location could no longer being exactly defined

The orbits proposed by Bohr were considered electron waves and the electron wave characteristics were directly related to the probability of the location of an electron The location of an electron was represented as a cloud (hence the reason the quantum mechanical model is sometimes referred to as the “electron cloud model”) These probability areas that represented a 95% probability of finding the electron in that area were now called atomic orbitals: area around the nucleus where an electron is likely to be found

In 1925, Werner Heisenberg suggested that it is impossible to know both the exact location and velocity of an electron at the same time That became known as the Heisenberg uncertainty principle It confirms the concept of even though matter, like light, has a dual nature, it cannot be both at the same time If you treat the electron like a particle, you can determine its location If you treat the electron like a wave, you can determine its velocity

Thus the quantum mechanical model of the atom is a largely mathematical treatment of the behavior of electrons in the area surrounding the nucleus The mathematics make it difficult to simplify