Quantum Theory & the Atom

Historical Development of quantum theory At the beginning of the 20th century light’s wave properties were well accepted but they theory was not able to account for everything.

The Problem of Black Body Radiation Why does a piece of iron glow at different colours when heated? First infra-red, then red, then yellow then white hot. What about the other colours in the spectrum?

Max Planck In 1900 Max Planck proposed a solution. If the energy was dispersed in defined packets of energy (he named them quanta, quantum singular) this could account for the specific colours that represented specific frequencies/wavelengths of energy. He defined these quanta as having the energy E = h E = energy h = constant (now named Planck’s constant)  = frequency of the light energy This theory was not well accepted when published

Einstein to the rescue! In 1905 Einstein solved a problem called the photoelectric effect using Planck’s idea of quanta The photoelectric effect is the phenomenon in which different colours of light have different effectiveness in expelling electrons from a metal’s surface. Einstein proposed that light consists of tiny packets of energy called photons whose effectiveness depends on their frequency. Ie violet light (higher frequency photons) is more powerful that red light with a lower frequency photons Einstein’s use of Planck’s idea popularized it

Dual Nature of Light This led to a greater understanding of light as having properties of both waves and particles Demonstrated in 1923 by Arthur Compton

Line Spectra Revisited The Bohr model of the atom was informed by the line spectrum of hydrogen The single electron in hydrogen must be in quantized orbits with different energies

Bohr Model Each orbit is a specific energy level An electron that is excited or gains energy jumps to a higher energy level, when it drops a level it releases a photon with a specific energy (IE colour) Quantum number (n) – the number given to the orbits Lowest energy n=1 (closest to nucleus) Ground state – element at its lowest energy level Bohr’s model worked well for hydrogen but not for elements with more than one electron

Matter Waves 1924 Louis De Broglie proposed wave behavior for particles breaking down the barrier between matter and energy Electrons move as waves Thus redefining the idea of an electron orbit

Heisenberg’s Uncertainty Principle 1927 Werner Heisenberg proposes that it is impossible to know both the position and momentum of an electron simultaneously Measurement of an electron’s position or movement alters its path in an unpredictable manner This leads to the idea that one can only talk about probabilities for the location and movement of electrons Atomic “Orbits” are calculated as probability clouds not defined orbits

Quantum Mechanical Model The energy of electrons is quantized Electrons exhibit wavelike behavior It is impossible to know the exact position and momentum of an electron at any given moment

Orbitals Since it is inaccurate to speak of electron paths with precise orbits the term orbital is used instead An Orbital is the region of probability around a nucleus for finding an electron with a particular energy Calculated orbitals have the appearance of a cloud

Orbital shapes Orbitals are designated by the letters s, p, d, f s orbitals are spherical p orbitals are dumbbell shaped The others are more complex

Orbitals & Energy Principal Energy levels – main energy levels found in quantum model n=1,2,3,… Determined by principal quantum number (like Bohr’s model) Unlike Bohr’s model they are further divided into sublevels The number of sublevels is determined by n for that energy level

Notice that there is overlap between different energy levels

Orbitals and Energy Levels Notice that each orbital type has a unique population in each energy level

Electron Spin In addition to energy electrons have a property called spin They can spin in either of two directions (clockwise or counterclockwise) These spins result in magnetic poles pointing in opposite directions Pauli Exclusion Principle (1925) – each orbital can hold a maximum of two electrons and they must have opposite spins Therefore each level has a maximum number of electrons