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The shape, size, and energy of each orbital is a function of 3 quantum numbers which describe the location of an electron within an atom or ion. n (principal) ---> energy level. l (orbital) ---> shape of orbital. ml (magnetic) ---> designates a particular suborbital. The fourth quantum number is not derived from the wave function. s (spin) ---> spin of the electron (clockwise or counterclockwise: ½ or – ½)

A Brief Introduction to Quantum Mechanics (and Quantum Numbers)

A Brief Introduction to Quantum Mechanics (and Quantum Numbers)

A Brief Introduction to Quantum Mechanics (and Quantum Numbers) Classical physics (also commonly known as Galilean physics) works quite well on the macro scale.  We can use Galilean physics to determine the velocity of a moving vehicle, the force of a 50kg ball falling from a building, how far from the launch point a poodle will land after you kick it and so many other things.  However, when we move down to the atomic scale, Galilean physics is a little inaccurate (okay, so it’s way inaccurate).  To compensate for this lack of accuracy, physicists developed quantum mechanics (also called wave mechanics) and as of today, it is the best description of the quantum world.  It started off when the Danish physicist Niels Bohr, assumed that the electron of hydrogen atom can contain only definite quantities of energy. Alternate parts of Bohr’s hypothesis were gotten scientifically from the laws of Galilean material science and were utilized to depict the conduct of particles having a charge. It became apparent that this approach was very inadequate.  Thus, quantum mechanics was born…

One important aspect of quantum mechanics is the Heisenberg Uncertainty Principle.  To predict the path of a moving object, we must be aware of both its momentum and its position.  According to the Heisenberg Uncertainty Principle, not only is it difficult, but it’s downright impossible to determine the exact position and the exact momentum simultaneously.  The greater accuracy we determine the measurement of one, the more uncertainty there is with the other.  Think of it this way.  Suppose we have a runner running around a track and we decide to take a picture of her.  If we took the picture of her with a high-speed film, there will be one set image of her (no blurring) and from there we can determine her position with respect to another object but we can’t determine how fast she is going.  But suppose we have taken a picture of her using a low-speed film.  The picture will contain our runner blurred.  Now while we can determine how fast she was going, it rather difficult to determine her position with respect to another object (this reminds me of a joke.  Heisenberg was speeding down a roadway when a cop pulls him over.  “you know how fast you were going buddy?”  Heisenberg looked at the cop and goes “no, but I know where I’m at”).

Another concept that helped push quantum mechanics into development was the dual nature of matter.  For many years, radiation (and in particular light) and the electron behaved like a wave in certain cases, and then like a particle (in light’s case, a photon).  Louis de Broglie, at that time a French doctoral student, suggested that the electron behaves as both a wave AND a particle.  If radiant energy under the adequate conditions can behave like particles, then, he concludes, couldn’t matter under appropriate conditions display wave-like properties?  De Broglie then went on to associate the wavelength (l) with its mass (m) and velocity (v) into a mathematical statement: l = (h)/(mv) where h is Planck’s Constant and the quantity mv is the momentum of any object.  Heisenberg’s Uncertainty Principle and De Broglie’s Hypothesis led the movement for a more applicable theory of the atomic structure as a whole.