1. Chapter 28 Atomic Physics Conceptual questions: 2,4,8,9,16
Quick quizzes: 1,2,3,4
Problems: 18, 39
Examples: 1,3,4

2. Rutherford’s Model of the Atom
Planetary model
Positive charge is concentrated in the center of the atom, called the nucleus
Electrons orbit the nucleus like planets orbit the sun

3. Examples of Spectra
a) emission b) absorption

4. Absorption Spectra
An element can also absorb light at specific wavelengths
The absorption spectrum consists of a series of dark lines superimposed on the otherwise continuous spectrum
The dark lines of the absorption spectrum coincide with the bright lines of the emission spectrum

5. Spectral Lines of Hydrogen
The Balmer Series has lines whose wavelengths are given by the preceding equation
Examples of spectral lines
n = 3, λ = nm
n = 4, λ = nm

6. Balmer’s Equation
The wavelengths of hydrogen’s spectral lines can be found from
RH is the Rydberg constant
RH = x 107 m-1
n is an integer, n = 1, 2, 3, …
The spectral lines correspond to different values of n

7. Bohr’s Assumptions for Hydrogen
Circular orbits around the proton under the influence of the Coulomb force of attraction
Only certain electron orbits are stable
Radiation is emitted by the atom when the electron “jumps” from a more energetic initial state to a lower state

8. Mathematics of Bohr’s Assumptions and Results
Electron’s orbital angular momentum
me v r = n ħ where n = 1, 2, 3, …
The total energy of the atom
Coulomb’s force provides centripetal acceleration
Radiation emitted, Ei – Ef = hf

9. Radii and Energy of Orbits
The radii of the Bohr orbits are quantized
n = 1, the orbit has the smallest radius, called the Bohr radius, ao
ao = nm
A general expression for the radius of any orbit in a hydrogen atom is
rn = n2 ao
The energy of any orbit is
En = eV/ n2

10. Energy Level Diagram
The value of RH from Bohr’s analysis is in excellent agreement with the experimental value
A more generalized equation can be used to find the wavelengths of any spectral lines

11. Generalized Equation
For the Balmer series, nf = 2
For the Lyman series, nf = 1
Whenever an transition occurs between a state, ni to another state, nf (where ni > nf), a photon is emitted
The photon has a frequency f = (Ei – Ef)/h and wavelength λ

12. Successes of the Bohr Theory
Explained several features of the hydrogen spectrum
Accounts for Balmer and other series
Predicts a value for RH that agrees with the experimental value
Gives an expression for the radius of the atom
Predicts energy levels of hydrogen
Gives a model of what the atom looks like and how it behaves
Can be extended to “hydrogen-like” atoms
Those with one electron
Ze2 needs to be substituted for e2 in equations
Z is the atomic number of the element

13. de Broglie Waves
In this example, three complete wavelengths are contained in the circumference of the orbit
In general, the circumference must equal some integer number of wavelengths
2  r = n λ n = 1, 2, …

14. Electron Clouds

15. Modifications of the Bohr Theory – Elliptical Orbits
Sommerfeld extended the results to include elliptical orbits
Retained the principle quantum number, n
Added the orbital quantum number, ℓ
ℓ ranges from 0 to n-1 in integer steps
All states with the same principle quantum number are said to form a shell
The states with given values of n and ℓ are said to form a subshell

16. Modifications of the Bohr Theory – Zeeman Effect
Another modification was needed to account for the Zeeman effect
The Zeeman effect is the splitting of spectral lines in a strong magnetic field
This indicates that the energy of an electron is slightly modified when the atom is immersed in a magnetic field
A new quantum number, m ℓ, called the orbital magnetic quantum number, had to be introduced
m ℓ can vary from - ℓ to + ℓ in integer steps

17. Quantum numbers for the hydrogen atom

18. QUICK QUIZ 28.1
In an analysis relating Bohr's theory to the de Broglie wavelength of electrons, when an electron moves from the n = 1 level to the n = 3 level, the circumference of its orbit becomes 9 times greater. This occurs because (a) there are 3 times as many wavelengths in the new orbit, (b) there are 3 times as many wavelengths and each wavelength is 3 times as long, (c) the wavelength of the electron becomes 9 times as long, or (d) the electron is moving 9 times as fast.

19. Quantum Number Summary
The values of n can range from 1 to  in integer steps
The values of ℓ can range from 0 to n-1 in integer steps
The values of m ℓ can range from -ℓ to ℓ in integer steps

20. QUICK QUIZ 28.2
How many possible orbital states are there for (a) the n = 3 level of hydrogen? (b) the n = 4 level?

21. QUICK QUIZ 28.3
When the principal quantum number is n = 5, how many different values of (a)  and (b) m are possible?

22. Modifications of the Bohr Theory – Fine Structure
High resolution spectrometers show that spectral lines are, in fact, two very closely spaced lines, even in the absence of a magnetic field
This splitting is called fine structure
Another quantum number, ms, called the spin magnetic quantum number, was introduced to explain the fine structure

23. Spin Magnetic Quantum Number
It is convenient to think of the electron as spinning on its axis
The electron is not physically spinning
There are two directions for the spin
Spin up, ms = ½
Spin down, ms = -½
There is a slight energy difference between the two spins and this accounts for the Zeeman effect

24. The Pauli Exclusion Principle
No two electrons in an atom can ever be in the same quantum state
In other words, no two electrons in the same atom can have exactly the same values for n, ℓ, m ℓ, and ms
This explains the electronic structure of complex atoms as a succession of filled energy levels with different quantum numbers

26. The Periodic Table
The outermost electrons are primarily responsible for the chemical properties of the atom
Mendeleev arranged the elements according to their atomic masses and chemical similarities
The electronic configuration of the elements explained by quantum numbers and Pauli’s Exclusion Principle explains the configuration

28. QUICK QUIZ 28.4
Krypton (atomic number 36) has how many electrons in its next to outer shell (n = 3)? (a) 2 (b) 4 (c) 8 (d) 18

29. Problems
18. A particle of charge q and mass m, moving with a constant speed v, perpendicular to a constant magnetic field, B, follows a circular path. If the angular momentum about the center of this circle is quantized so that mvr = nħ , show that the allowed radii for the particle are
where n = 1, 2, 3, . . .
39. Zirconium (Z = 40) has two electrons in an incomplete d subshell. (a) What are the values of n and l for each electron? (b) What are all possible values of ml and ms ? (c) What is the electron configuration in the ground state of zirconium?

30. Characteristic X-Rays

31. Explanation of Characteristic X-Rays
The details of atomic structure can be used to explain characteristic x-rays
A bombarding electron collides with an electron in the target metal that is in an inner shell
If there is sufficient energy, the electron is removed from the target atom
The vacancy created by the lost electron is filled by an electron falling to the vacancy from a higher energy level
The transition is accompanied by the emission of a photon whose energy is equal to the difference between the two levels

32. Atomic Transitions – Energy Levels
An atom may have many possible energy levels
At ordinary temperatures, most of the atoms in a sample are in the ground state
Only photons with energies corresponding to differences between energy levels can be absorbed

33. Atomic Transitions – Stimulated Absorption
The blue dots represent electrons
When a photon with energy ΔE is absorbed, one electron jumps to a higher energy level
These higher levels are called excited states
ΔE = hƒ = E2 – E1
In general, ΔE can be the difference between any two energy levels

34. Atomic Transitions – Spontaneous Emission
Once an atom is in an excited state, there is a constant probability that it will jump back to a lower state by emitting a photon
This process is called spontaneous emission

35. Atomic Transitions – Stimulated Emission
An atom is in an excited stated and a photon is incident on it
The incoming photon increases the probability that the excited atom will return to the ground state
There are two emitted photons, the incident one and the emitted one
The emitted photon is in exactly in phase with the incident photon

36. Lasers To achieve laser action, three conditions must be met
The system must be in a state of population inversion
The excited state of the system must be a metastable state
Its lifetime must be long compared to the normal lifetime of an excited state
The emitted photons must be confined in the system long enough to allow them to stimulate further emission from other excited atoms
This is achieved by using reflecting mirrors

37. Production of a Laser Beam

38. Laser Beam – He Ne Example
The energy level diagram for Ne
The mixture of helium and neon is confined to a glass tube sealed at the ends by mirrors
A high voltage applied causes electrons to sweep through the tube, producing excited states
When the electron falls to E2 in Ne, a nm photon is emitted

39. Conceptual questions
2.Does a light emitted by a neon sign constitute a continuous spectrum or only a few colors.
4. Must an atom first be ionized before it can emit light?
8. If matter has a wave nature, why is this not observable in our daily experiences?
9. Discuss consequences of the exclusion principle.
16. A 1 mW laser might damage your eye if you look directly at it, but there is no harm at looking directly at a 100 W lightbulb. Why?

40. Energy Bands in Solids Sodium example
Blue represents energy bands occupied by the sodium electrons when the atoms are in their ground states
Gold represents energy bands that are empty
White represents energy gaps
Electrons can have any energy within the allowed bands
Electrons cannot have energies in the gaps

41. Energy Level Definitions
The valence band is the highest filled band
The conduction band is the next higher empty band
The energy gap has an energy, Eg, equal to the difference in energy between the top of the valence band and the bottom of the conduction band

42. Conductors
When a voltage is applied to a conductor, the electrons accelerate and gain energy
In quantum terms, electron energies increase if there are a high number of unoccupied energy levels for the electron to jump to
For example, it takes very little energy for electrons to jump from the partially filled to one of the nearby empty states

43. Insulators The valence band is completely full of electrons
A large band gap separates the valence and conduction bands
A large amount of energy is needed for an electron to be able to jump from the valence to the conduction band

44. Semiconductors A semiconductor has a small energy gap
Thermally excited electrons have enough energy to cross the band gap
The resistivity of semiconductors decreases with increases in temperature
The white area in the valence band represents holes

45. Semiconductors, cont
Holes are empty states in the valence band created by electrons that have jumped to the conduction band
Some electrons in the valence band move to fill the holes and therefore also carry current
The valence electrons that fill the holes leave behind other holes
It is common to view the conduction process in the valence band as a flow of positive holes toward the negative electrode applied to the semiconductor

46. Current Process in Semiconductors
An external voltage is supplied
Electrons move toward the positive electrode
Holes move toward the negative electrode
There is a symmetrical current process in a semiconductor

47. Doping in Semiconductors
Doping is the adding of impurities to a semiconductor
Generally about 1 impurity atom per 107 semiconductor atoms
Doping results in both the band structure and the resistivity being changed

48. A p-n Junction
A p-n junction is formed when a p-type semiconductor is joined to an n-type
Three distinct regions exist
A p region
An n region
A depletion region

49. Diode Action
The p-n junction has the ability to pass current in only one direction
When the p-side is connected to a positive terminal, the device is forward biased and current flows
When the n-side is connected to the positive terminal, the device is reverse biased and a very small reverse current results

50. Applications of Semiconductor Diodes
Rectifiers
Change AC voltage to DC voltage
A half-wave rectifier allows current to flow during half the AC cycle
A full-wave rectifier rectifies both halves of the AC cycle
Transistors
May be used to amplify small signals
Integrated circuit
A collection of interconnected transistors, diodes, resistors and capacitors fabricated on a single piece of silicon