PH 103 Dr. Cecilia Vogel Lecture 20

Review Outline  Quantum numbers  H-atom  spectra  uncertainty  atoms and nuclei  The quantum model of the atom

Current Model of Atom  Electron “cloud” is wavefunction  describes the probability of electron being at various points around the nucleus.  Electron wave behavior based on  Schroedinger equation.  The electron states are quantized  4 different quantities are quantized  4 different quantum numbers  n, ℓ, m ℓ, m s. 

Four Quantum Numbers Quantum number Physical quantity Possible values Additional restrictions n ℓ mℓmℓ msms Energy Size of orbital Positive integers n > ℓ Orbital angular momentum (Energy) Non-negative integers ℓ < n ℓ > |m ℓ | Orb. ang. mom. z-component integers |m ℓ | < ℓ Spin z-component + ½ or - ½none

Principle Quantum Number  Principle quantum number, n,  n = 1, 2, 3, 4, 5,....  Determines what “shell” the electron is in.  n=1 is called the K-shell,  n=2 is the L-shell, etc  tells a lot about the electron’s energy  for hydrogen atom, it determines the electron’s energy  for hydrogen atom:

Hydrogen Ground State  Consider the electron in hydrogen  the ground state is the lowest energy state  lowest E, lowest n, n = 1  Since n =1, then = 0  Since = 0, then m = 0  m s =  ½ (2 possibilities)  Ground state has a degeneracy of two  because there are two states with the same E

Transition Up  Electron absorbs energy  perhaps from a photon  goes to a higher energy level e-e- photon e-e-

Transition Up  Some ways to add energy to the atom  i.e. ways to excite electron:  HEAT  like blackbody radiation  ZAP  electric discharge through a gas  SLAM  hit atom with high-energy particle  for example, nuclear radiation  SHINE  hit atom with light (photons)

Transition Down – H-atom  Electron loses energy to a photon - - gives off light  Electron goes to a lower energy level  losing energy e-e- e-e- photon

Transition Down – H-atom  Electron loses energy to a photon - - gives off light  Light created has the energy that the electron lost  so

Hydrogen spectrum  Visible lines in H-spectrum  come from transitions to n f =2.  Ex: with n i =3

H and Multi-electron Atoms  Recall for Hydrogen  electron Energy depends on n only  Other atoms  electron energy depends on n and ℓ  So…  L-shell (n=2) for hydrogen atom  is just one energy level  L-shell for other atoms  -- two different energy levels  2s and 2p  and M-shell splits into 3s, 3p, 3d subshells, etc

Single-electron atoms (like Hydrogen) Other atoms

Compare Hydrogen to Multi-electron Atoms  Hydrogen has  few e - energy levels  few e - transitions  few photon energies, few wavelengths  Other atoms  many e - energy levels  many e - transitions  many photon energies, many wavelengths  generally have more complicated spectrum