QUANTUM MECHANICS VIEW OF THE ATOM

Werner Heisenberg Werner Heisenberg proposed a theory in 1927 known as the uncertainty principle.  It argued that since we have to use light to identify the location or motion of an electron, the photon of light will influence the electron's motion and position.  The uncertainty principle says the more certain we are about a particle's position, the less certain we are about its momentum (mass x velocity), and vice versa. 

Louis de Broglie :if radiant energy could, under appropriate circumstances behave as though it were a stream of particles, then could matter, under appropriate circumstances, exhibit wave-like properties? For example, the electron in orbit around a nucleus. DeBroglie suggested that the electron could be thought of as a wave with a characteristic wavelength.

QUANTUM NUMBERS Variables in Schrodinger’s equations with solutions that give information about the probable location of an electron.

Principle Quantum Number (n) has integral values 1, 2, 3, ...... The principle quantum number is related to size of the electron cloud (distance from the nucleus that the electron is 90% of the time) and energy of the orbital. The larger the value of n the more time the electron spends further from the nucleus and the higher the energy. n = energy level.

Angular Momentum Quantum Number (l) has integral values {0 to n-1}. This quantum number gives us the shape of the probability pattern and each shape is referred to as a sublevel. Each sublevel has a letter designation and a numerical value. s 0 p 1 d 2 f 3

When l = 0, the orbital is a sphere. It is known as an “s” orbital.

When l= 1, the orbital is dumbbell shaped When l= 1, the orbital is dumbbell shaped. The orbital is known as a “p” orbital.

When l = 2, the orbital can exist in either of two forms When l = 2, the orbital can exist in either of two forms. It can be a cloverleaf pattern or a dumbbell with a donut. In both cases, the orbital is called a “d” orbital.

When l = 3, the orbital type is called a “f ” orbital.

Magnetic Quantum Number The Magnetic quantum number refers to the possible orientations in space of each orbital. (m) has integral values {-l to +l}. Each different orientation of a sublevel is a different orbital. In the p sublevel l = 1 and ml = -1, 0, 1. Each of the values of the magnetic quantum number represents a different p orbital px, py, and pz. The p orbitals differ in their orientation.

For an “s” orbital l = 0 and ml = 0 Only 1 possible orientation for “s” orbitals. There can only be 1 “s” orbital in any energy level.

For “p” orbitals l = 1 and ml = {-1, 0, 1} There are 3 possible orientations for “p” orbitals. Any energy level that ”p” orbitals occupy can have 1 to 3 “p” orbitals.

For “d” orbitals l = 2 and ml = {-2, -1, 0, 1, 2} There can be 1 to 5 “d” orbitals in any energy levels that can have “d” orbitals.

For “f’” orbitals l = 3 and ml = {-3, -2, -1, 0, 1, 2, 3} An energy level that can have “f” orbitals can have 1 to 7 “f” orbitals.

Magnetic Spin Quantum Number S or ms differentiates the two electrons that can exist in a single orbital and has the value of +1/2 or -1/2. Spin can be interpreted as the electron’s rotation either clockwise or counter-clockwise around an axis. A SINGLE ORBITAL CAN HOLD A MAXIMUM OF 2 ELECTRONS. Pauli’s Exclusion Principle = no two electrons in an atom have the same set of quantum numbers.

Energy Level 1 2 3 4 Sublevel s s, p s,p,d s, p, d, f # e- in each sublevel 2,6 2,6,10 2, 6, 10 ,14 Total # of e- in each energy level 8 16 32