PHYS 221 Recitation

Kevin RalphsWeek 13

Overview

• Atomic Theory– Pre-Quantized Atomic Models– Atomic Spectra– The Bohr Model– Wave Mechanics and the Hydrogen Atom– Multielectron Atoms– Periodic Table– Applications

Atomic Theory

• Pre-Quantized Atomic Models– Plum-Pudding Model

• Experiments first showed that atoms contained removable negative electric charges, electrons

• However, non-ionized atoms are electrically neutral so there must be some amount of positive charge that balances the electron’s charge

• It was originally thought that the positive charge was evenly distributed throughout the volume of the atom

• Confirmation of this model was soughtafter by Rutherford using alpha particlescattering which implied that the positivecharge was centrally located

Atomic Theory• Pre-Quantized Atomic Models (cont.)

– The Planetary Model• The existence of the atomic nucleus and the discovery of the proton are

actually two separate discoveries, although both by Rutherford’s scattering experiments

• He showed that he could “knock” hydrogen nuclei out of other atoms with Z, the atomic number, describing how many hydrogen nuclei an atom had

• We now know that the nucleus is made up of both protons and neutrons with the neutron stabilizing the nucleus

• The planetary model assumes that theelectrons in an atom move around it like planets held in orbit by the Coulomb force

• Although it was wrong, it was an importantstepping stone to us understanding the atom

Atomic Theory• Atomic Spectra

– A normal blackbody spectrum has nosudden dips in it so we would expect the sun, an approximate blackbody, to have such a spectrum, but this is not the case. The gas in the sun and our atmosphere is absorbing that light

– Additionally, we noticed that if we electrically excited gases that they only emitted light at specific frequencies

– The interesting thing we found was that the absorption and emission lines for a gas line up

– This was a problem for the planetary model because an electron orbit can have a continuous range of energies so why did absorption and emission have discrete spectra?

Atomic Theory

• The Bohr Model– Bohr assumed that the angular momentum of

electron orbits was evenly spaced giving the following quantization:

– Using this with the planetary model and assuming

circular orbits, he was able to derive an expression for the different electron radii using Newtonian mechanics

Atomic Theory

• The Bohr Model (cont.)– From here, the energy of the electron can be calculated

– This correctly predicts the ionization energy and the energy spectrum of hydrogen

– De Broglie reasoned that this was due to electrons needing to form standing waves in their orbits

– It should be noted that not everything is quantized in quantum theory. If a photon has more than 13.6 eV in energy, the electron will be ejected so any photon above this can be absorbed giving a continuous energy spectrum

Atomic Theory

• Wave Mechanics and the Hydrogen Atom– Eventually in the 1920s, the nascent quantum

mechanics was applied to the hydrogen atom– Two versions, wave mechanics proposed by Erwin

Schrodinger and matrix mechanics put forth by Heisenberg were used to explain things

– The mathematics, of course, are beyond the scope of this course, but it led to certain numbers that could be used to classify electrons as they were bound to atomic nuclei

Atomic Theory• Wave Mechanics and the Hydrogen Atom (cont.)

– There are four quantum numbers that we can use to completely classify the state of a bound electron in an atomic nuclei (ie the electron orbital)• n, the principle quantum number: n begins at 1, and gives the energy of an

electron when there are no external electric or magnetic fields present; it also can be viewed as describing the average distance of the electron from the nucleus and is referred to as an “n shell”

• l is the orbital quantum number: This describes the amount of orbital angular momentum the electron has and can go from 0 to n-1. Letters are often used to describe this: l = 0 is an s state, while l = 1 is a p state.

• m aka is the orbital magnetic quantum number which goes from m = -l to m = l can be thought of as describing the quantization of the direction of the angular momentum

• s aka is the spin quantum number and describes the direction of the angular momentum of the spin

Atomic Theory

• The hydrogen wave function can be broken into two parts: one that gives the angular distribution and one that gives the radial distribution. When combined they are the following:

Atomic Theory

• Multielectron Atoms– When there are multiple electrons bound to an atom, the

same quantum numbers apply, but only one electron can have a specific set of quantum numbers

– This is known as the Pauli Exclusion Principle and has to do with the fact that the electron has an odd half multiple for its spin

– Electron configurations are denoted by the number of electrons in each combination of n, l numbers

Electron configuration for C:

Atomic Theory• Periodic Table

– The periodic table was developed before quantum mechanics and organizes elements by the kinds of chemical reactions they take part in

– The elements in each group (column) behave similarly and are then sorted in the group by mass

– The gaps in the table had no real explanation until the full quantum treatment of the atom

– We now know that it is the valenceelectrons in an open shell that participatein chemical reactions

– It is extremely difficult to remove electrons from a closed shell so theyare normally inert

Quiz Question

How much energy is needed to ionize a hydrogen atom that is initially in the n = 4 state?

a) 3.4 eVb) 0.85 eVc) 6.8 eVd) 13.6 eV

Quiz Question

What is the total number of electron states in the n = 3 shell?

a) 4b) 8c) 9d) 16e) 18

Quiz Question

What are the allowed values of for the n = 5 shell?

a) 0, 1, 2, 3, 4b) 0, 1, 2, 3, 4, 5c) -4, -3, -2, -1, 0, 1, 2, 3, 4d) -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

Quiz Question

Give the electron configuration for Silicon (Z = 14) in the ground state

a) b) c) d) e)