1. Chapter 28 Atomic Physics

2. General Physics Atom Physics Sections 1–4

3. General Physics Importance of Hydrogen Atom Hydrogen is the simplest atom Enables us to understand the periodic table Ideal system for performing precise comparisons of theory with experiment Much of what we know about the hydrogen atom can be extended to other single-electron ions For example, He + and Li 2+

4. General Physics Sir Joseph John Thomson “J. J.” Thomson 1856 - 1940 Developed model of the atom Discovered the electron Did extensive work with cathode ray deflections 1906 Nobel Prize for discovery of electron

5. General Physics Early Models of the Atom Newton’s model of the atom was a tiny, hard, indestructible sphere J.J. Thomson’s model of the atom A volume of positive charge Electrons embedded throughout the volume

6. General Physics Rutherford’s Scattering Experiments The source was a naturally radioactive material that produced alpha particles (He ++ ) Most of the alpha particles passed though the gold foil A few deflected from their original paths Some even reversed their direction of travel Active Figure: Rutherford ScatteringRutherford Scattering

7. General Physics Rutherford Model of the Atom Rutherford, 1911 Planetary model Based on results of thin foil experiments Positive charge is concentrated in the center of the atom, called the nucleus Electrons orbit the nucleus like planets orbit the sun

8. General Physics Rutherford Model, Problems Atoms emit certain DISCRETE characteristic frequencies of electromagnetic radiation The Rutherford model is unable to explain this phenomena Rutherford’s electrons are undergoing a centripetal acceleration and so should radiate electromagnetic waves at a frequency related to their orbital speed The radius should steadily decrease and the speed should steadily increase as this radiation is given off The electron should eventually spiral into the nucleus, but it doesn’t The radiation frequency should steadily increase – should observe a continuous spectrum of radiation at progressively shorter and shorter wavelengths, but you don’t

9. General Physics Emission Spectra When a high voltage is applied to a gas at low pressure, it emits light characteristic of the gas When the emitted light is analyzed with a spectrometer, a series of discrete bright lines is observed - emission spectrum Each line has a different wavelength and color

10. General Physics Emission Spectrum of Hydrogen – Equation The wavelengths of hydrogen’s spectral lines experimentally agree with the equation R H is the Rydberg constant R H = 1.0973732 x 10 7 m -1 n is an integer, n = 3, 4, 5, 6, … The spectral lines correspond to different values of n

11. General Physics Spectral Lines of Hydrogen The Balmer Series has lines whose wavelengths are given by the preceding equation Examples of spectral lines n = 3, λ = 656.3 nm n = 4, λ = 486.1 nm n = 5, λ = 434.1 nm n = 6, λ = 410.2 nm

12. General Physics Absorption Spectra An element can also absorb light at specific wavelengths An absorption spectrum can be obtained by passing a continuous radiation spectrum through a vapor of the gas 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

13. General Physics Applications of Absorption Spectrum The continuous spectrum emitted by the Sun passes through the cooler gases of the Sun’s atmosphere The various absorption lines can be used to identify elements in the solar atmosphere Led to the discovery of helium

14. General Physics Neils Bohr 1885 – 1962 Participated in the early development of quantum mechanics Headed Institute in Copenhagen 1922 Nobel Prize for structure of atoms and radiation from atoms

15. General Physics The Bohr Theory of Hydrogen In 1913 Bohr provided an explanation of atomic spectra that includes some features of the currently accepted theory His model includes both classical and non- classical ideas His model included an attempt to explain why the atom was stable

16. General Physics Bohr’s Assumptions for Hydrogen The electron moves in circular orbits around the proton under the influence of the Coulomb force of attraction The Coulomb force produces the centripetal acceleration Only certain electron orbits are stable These are the orbits in which the atom does not emit energy in the form of electromagnetic radiation

17. General Physics Bohr’s Assumptions, cont Radiation is emitted by the atom when the electron “jumps” from a more energetic initial state to a lower state The frequency emitted in the “jump” is related to the change in the atom’s energy It is generally not the same as the frequency of the electron’s orbital motion The size of the allowed electron orbits is determined by a condition imposed on the electron’s orbital angular momentum L n = m e v r = n ħ where n = 1, 2, 3, …

18. General Physics Bohr Radius The radii of the Bohr orbits are quantized This is based on the assumption that the electron can only exist in certain allowed orbits determined by the integer n When n = 1, the orbit has the smallest radius, called the Bohr radius, a o a o = 0.0529 nm

19. General Physics Quantized Energies The total energy of the atom Using the radius equation for the allowed Bohr orbits When n = 1, the orbit has the lowest energy, called the ground state energy E 1 = -13.6 eV

20. General Physics Radii and Energy of Orbits A general expression for the radius of any orbit in a hydrogen atom is r n = n 2 a o The energy of any orbit is E n = - 13.6 eV/ n 2

21. General Physics Specific Energy Levels The lowest or ground state energy level has an energy of –13.6 eV The next energy level has an energy of –3.40 eV The energies can be compiled in an energy level diagram The ionization energy is the energy needed to completely remove the electron from the atom The ionization energy for hydrogen is 13.6 eV The uppermost level corresponds to E = 0 and n  

22. General Physics Energy Level Diagram & Equation Whenever a transition occurs from a state, n i to another state, n f (where n i > n f ), a photon is emitted The photon is emitted with energy hf = (E i – E f ) with a wavelength λ given by For the Paschen series, n f = 3 For the Balmer series, n f = 2 For the Lyman series, n f = 1 Active Figure: Bohr's Model of the Hydrogen AtomBohr's Model of the Hydrogen Atom

23. General Physics Bohr’s Correspondence Principle Bohr’s Correspondence Principle states that quantum mechanics is in agreement with classical physics when the energy differences between quantized levels are very small Similar to having Newtonian Mechanics be a special case of relativistic mechanics when v << c

24. General Physics Successes of the Bohr Theory Explained several features of the hydrogen spectrum Accounts for Balmer and other series Predicts a value for R H 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 Ze 2 needs to be substituted for e 2 in equations Z is the atomic number of the element

25. General Physics Modifications of the Bohr Theory – Elliptical Orbits Sommerfeld extended the results to include elliptical orbits Retained the principle quantum number, n Determines the energy of the allowed states 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

26. General Physics 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

27. General Physics 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, m s, called the spin magnetic quantum number, was introduced to explain the fine structure There are two directions for the spin Spin up, m s = ½ Spin down, m s = -½

28. General Physics Number of Electrons in Filled Subshells and Shells (First Three Shells) Shell - principle quantum number Subshell - orbital quantum number orbital magnetic quantum number spin magnetic quantum number Electrons in Filled Subshell Electrons in Filled Shell K ( n = 1 )s ( ℓ = 0 )m ℓ = 0 m s = + ½, − ½ 22 L ( n = 2 ) s ( ℓ = 0 )m ℓ = 0 m s = + ½, − ½ 2 8 p ( ℓ = 1 )m ℓ = +1, 0, −1 m s = + ½, − ½ 6 M ( n = 3 ) s ( ℓ = 0 )m ℓ = 0 m s = + ½, − ½ 2 18 p ( ℓ = 1 )m ℓ = +1, 0, −1 m s = + ½, − ½ 6 d ( ℓ = 2 )m ℓ = +2, +1, 0, −1, −2 m s = + ½, − ½ 10

29. General Physics Atomic Transitions – Stimulated Absorption 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 = E 2 – E 1 In general, ΔE can be the difference between any two energy levels

30. General Physics 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

31. General Physics Atomic Transitions – Stimulated Emission An atom is in an excited stated and a photon is incident on it The incoming photon stimulates the excited atom to return to the ground state There are two emitted photons, the incident one and the emitted one The emitted photon has the same wavelength and is in phase with the incident photon Active Figure: Spontaneous and Stimulated EmissionSpontaneous and Stimulated Emission

32. General Physics Population Inversion When light is incident on a system of atoms, both stimulated absorption and stimulated emission are equally probable Generally, a net absorption occurs since most atoms are in the ground state If you can cause more atoms to be in excited states, a net emission of photons can result This situation is called a population inversion

33. General Physics Lasers To achieve laser action, three conditions must be met The system must be in a state of population inversion More atoms in an excited state than the ground state 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

34. General Physics Laser Beam – He Ne Example The energy level diagram for Ne in a He-Ne laser 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 E 2 from E* 3 in Ne, a 632.8 nm photon is emitted

35. General Physics Production of a Laser Beam

36. General Physics Holography Holography is the production of three-dimensional images of an object Light from a laser is split at B One beam reflects off the object and onto a photographic plate The other beam is diverged by Lens 2 and reflected by the mirrors before striking the film

37. General Physics Holography, cont The two beams form a complex interference pattern on the photographic film It can be produced only if the phase relationship of the two waves remains constant This is accomplished by using a laser The hologram records the intensity of the light and the phase difference between the reference beam and the scattered beam The image formed has a three-dimensional perspective