The Quantum Model Section 4.2

Bell Work A spherical electron cloud surrounding an atomic nucleus would best represent a _____ sublevel. Any one (1) atomic orbital can hold a maximum of ___ electrons An energy level of n=2 contains ____ orbitals. An energy level of n=4 contains ____ orbitals. An energy level of n=3 can hold ____ electrons. An energy level of n=1 can hold ____ electrons. An f - sublevel can hold ____ electrons.

Bell Work Define Diffraction. Define Interference. Define Orbitals. List the 4 quantum numbers. What is the frequency of a wave with 2.56 X 1013 meters wavelength. What is the energy of a wave with a wavelength of 6.45 X 10-16.

Intro Scientist did not believe Bohr’s model. If the e - orbit starts to decay, the e - would be sucked into the nucleus. Why couldn’t the electron exist in limitless number of orbits with slightly different energies.

Electrons as waves The photoelectric effect revealed light could behave both as a wave and a particle. Could e - behave this way also??

Electrons as waves Louis de Broglie: 1924 he hypothesized De Broglie’s hypothesis: e - behave both as waves and particles. He felt e - should be considered waves confined to space and that they exist in only certain frequencies. Through experiments, e - were shown to exhibit two wave-like properties.

Two wave-like properties that strengthened de Broglie’s hypothesis: Diffraction: refers to the bending of a wave as it passes by the edge of an object Interference: overlapping of waves resulting in an increase of energy in some areas and a decrease of energy in other areas.

Werner Heisenberg Werner Heisenberg – 1927 he was experimenting with photons trying to detect if e - even existed. Heisenberg Uncertainty Principle: states that it is impossible to determine simultaneously both the position and velocity of an e - (or any other particle).

Erwin Schrodinger Erwin Schrödinger: he used de Brolgie’s hypothesis to develop a mathematical formula that treats e - as waves. Schrödinger Wave Equation – is what the formula became known as and it, along with Heisenberg Uncertainty Principle, laid the foundation for the modern Quantum Theory.

Schrodinger’s wave Equation

Quantum Theory Quantum Theory: Describes mathematically the wave properties of e - (and other particles). The solutions (or wave functions) give only the probability of finding an e - at a given place at a given time. e - do not travel around the nucleus in neat orbits but in regions called orbitals.

Orbitals Orbital – are three dimensional regions around the nucleus that suggest the probable location of an e -.

Atomic Orbitals & Quantum #s Quantum Numbers: specify the properties of atomic orbitals and the properties of the electrons in those orbitals. There are four (4) quantum numbers.

Principal Quantum Number (n): indicates the energy level occupied by the electrons. n is always a positive #; 1,2,3 etc. More than 1 e – can exist in the same energy level (or electron shell) The total # of orbital in a given energy level is equal to n2 .

Angular Momentum Number (∫) – starting with the 2nd energy level, each energy level has different shaped orbitals called sublevels. ∫ indicates the shape of the sublevel. The number of sublevels in each energy level equals (n) or the number of that energy level . Example: in the 2 energy level, there are 2 sublevels

Magnetic Quantum Number (m) – indicates the orientation of an orbital. the s orbital is a sphere and has only one orientation. Therefore the m valve is 0. # of orbitals equal n2. Each higher sublevel will have 2 more orientation that the sublevel below it.

Spin Quantum Number – electrons in an orbital are though of as spinning on an internal axis. It spins in one of two directions. an electron has only two possible fundamental spin states in an orbital a single orbital can hold a maximum of 2 electrons, and they must have opposite spins