University:
Boston University
Course:
CAS PY 105 | Physics 1
Academic year:

2020
Views:

112

Pages:

2
Author:

stardumomentp9g1

Quantum Numbers Wavefunctions, Quantum Numbers, and the nature of electrons Electrons in atoms behave as waves (delocalized). Attempts to “measure” e–’s cause them to localize (particle). The picture in the book is the result of many electrons measured! 1 electron (b) = 1 dot in (a) The Wavefunction (𝜓) of an electron is the MATHEMATICAL function describing the electron wave. Just like sin(𝑥) describes a 1D wave, 𝜓 is a function of 𝑛, 𝑙, 𝑚! , 𝑚" : that describes the 3D wave that IS the electron. 𝑛, 𝑙, 𝑚! , 𝑚" are the quantum numbers that describe the wave! 1 Quantum numbers (n, l) n = total # of loops (or # nodes–1) (principal quantum number) ⟶ Energy of the wave: En = –(2.18 aJ)Z2/n2 ⟶ Size of the wave: radius = 52.9 pm n2/Z l = # of nodal planes (0, …, n–1) (azimuthal quantum number) ⟶ Wave of the shape (sphere, dumbbell, etc) 2 1 Quantum Numbers Quantum numbers (𝑚4 , 𝑚5 ) ml magnetic quantum number 0, ±1, … ±l (ml is about the orientation) (Check out falstad.com/qmatom to visualize them!) pz dz2 ml = 0: ml = ±1: px, py dxz dyz ml = ±2: dx2-y2 dxy ms spin quantum number -½, +½ Nothing is spinning!! This is an intrinsic property of the electron (no reason) – magnets have two orientations, so too here. 3 Common parlance and notation Electron: unique set of 4 QN’s (n, l, m l, m s) that describe a unique wave § Two electrons cannot have the same set of QNs (Pauli exclusion principle) § The electron IS the WAVE (e.g., 𝜓!" , 𝑚 " =+1/2) Orbital: the unique set of first three QNs for an electron in an atom (n, l, and m l) § There can be exactly two electrons with the same (n, l, and m l) § The electron isn’t IN in the orbital; orbitals aren’t places!! (e.g., 𝜓 #$!" ) Subshell: subset of the orbitals with the same energy and shape (n and l) § e.g., 2p subshell is 2px + 2py + 2pz; 4d subshell is 4dxy, 4dzy, 4dxz, 4dx2-y2, 4dz2 Shell: set of (degenerate, in H) orbitals (same energy, same n) 4 2