CHM 101 1st Edition Lecture 15Lecture 13 OverviewI. Electronic Structure of AtomsII. Quantized EnergyIII. Atomic SpectraIV. Bohr’s Model of the Hydrogen atomLecture 14I. The Wave Behavior of MatterII. Quantum MechanicsIII. Schrodinger’s ModelWave Behavior of Matter• Broglie figured that by treating electron orbits as standings waves it could explain whyonly certain levels were allowed• Broglie’s equationo λ = h/mv o mv – velocity o λ – de Broglie’s wavelengthThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.o this formula is given on tests• Macroscopic objects have large masses so their wave-like behavior is not importan• Electrons exhibit wave-like behavior • Example :o What is the wavelength of an electron moving with a speed of 5.99 x 106 m/s? The mass of the electron is 9.11 x 10-34 kgo λ = 6.63 x 10-34 J s x 1 kg m2/s2 = 1.22 x 10-10 m (9.11x10-34)(5.97 x 106 m/s) 1 JQuantum Mechanics • 1926 Erwin Schrodinger came up with a new model treating electrons as waves • Ψ2 – the probability density or electron density • The higher density of dots, in a drawing of an x and y axis graph with a concentration of dots in the middle, are where electrons are more likely to beOrbitals and Quantum numbers • Bohr’s model – electron circles around the nucleus• Schrodinger’s model – electron is somewhere within that spherical region• Bohr’s model – only one quantum number (n) needed to describe an orbit • Schrodinger’s model – requires 3 quantum numbers to describe an orbitalo n – principal quantum numbero ι – angular momentum quantum numbero mι– magnetic quantum number• Principal quantum number o Describes the general size of an orbitalo As the principal quantum number increases so does the orbital sizeo Electrons is orbitals with the same value of the principal quantum number are said to be in the same shello Allowed values of n – 1, 2, 3, 4, …• Angular Momentum quantum numbero General shape of an orbitalo Combination of n and ι define a subshello Allowed values of ι = n-1 = 0, 1, 2, 3, …o Each value of ι has a letter designation ι = 0 s orbital ι = 1 p orbital ι = 2 d orbital ι = 3 f orbital• Magnetic quantum numbero The orientation of an orbital in spaceo Allowed values of mι = -ι, … 0 … +ιo Example : ι = 1 then mι= -1, 0, 1o There are 3 possible orientations for p orbital ι =