3.6-3.7 textbook notes

3.6: Quantum Numbers:

• Wave mechanics/Quantum mechanics: a mathematical description of the wavelike behavior of particles on the atomic level

• Schrodinger wave equation: a description of how the electron matter wave varies with location and time around the nucleus of a hydrogen atom

• Wave functions: a solution to the Schrödinger wave equation

  • Describe how the matter wave of an electron in an atom varies in both time and location inside the atom

  • define the energy levels in hydrogen atom

• Orbital: a region around the nucleus of an atom where the probability of finding an electron is high; each orbital is defined by the square of the wave function

• Born could use his calculation to calculate the probability of electron transitions between orbitals

• Quantum numbers: one of four related numbers that specify the energy, shape, and orientation of orbitals in the atom and the spin orientation of electrons in the orbitals

  • n (principal quantum numbers): Positive integer that indicates relative size and energy of an orbital or of a group of orbitals in an atom

    • Orbitals with same value of n are in same shell

    • larger n = larger distance from the nucleus and higher energies than those with smaller n

  • Angular momentum quantum number, (l looped thing can’t type it out): an integer with a value ranging from zero to (n-1) that defines the shape of an orbital

    • Orbitals with same n and looped l are int he subshell and have the same energy

    • Identified with a letter:

      • 0 = s

      • 1 = p

      • 2 = d

      • 3 = f

      • 4 = g

  • Magnetic quantum number, M subscript looped l: an integer with a value from -looped l to + looped l

    • Defines the orientation of an orbital in the space around the nucleus of an atom

• in 3p: 3 is n and p is the looped 

• Can have different m looped l values because the orbitals can be shaped differently

• Spin quantum number (m subscript s): either +1/2 or -1/2 indicating the spin orientation of an electron

  • only two values +1/2 for spin up and -1/2 for spin down

• Pauli exclusion principle: the principle that no two electrons in an atom can have the same set of four quantum numbers

3.7: The sizes and Shapes of atomic orbitals: 

• Hydrogen atom is an onion, many layers all of the same thickness

• layer close to nucleus accounts for small amount of radius, which is why we go to the furthest level

• electron densities higher closer to the nucleus, volumes of spherical shells closest to nucleus are small that the electron will almost never be near the center of the atom

  • Still small chance, just very very small chance

• Greater distances, volume is large, but trident squared drops to zero

  • so, the chances of finding electrons in layers far from nucleus are small. 

• s orbitals are pretty high distance from the nucleus