Line Spectra When the particles in the solid, liquid, or gas accelerate, they will produce EM waves. Electron orbit to orbit transitions in atoms (gasses) Applicable to the study of stars (gaseous objects)

Line Spectra Atomic Structure Shell model of the atom (Bohr): electrons orbit the nucleus in hierarchy of stable orbits, each corresponding to a specific amount of electron energy. E1E1 E2E2 E3E3

Line Spectra Atomic Structure The normal state of the atom has the electron in the lowest energy orbit, called the ground state. The energy associated with the ground state is called the ground state energy. E1E1 E2E2 E3E3

Line Spectra Atomic Structure Energy Minimum Principle: An electron in orbit around a nucleus will orbit in the lowest available energy orbit. E1E1 E2E2 E3E3

Line Spectra Atomic Structure Exclusion Principle: No two electrons can exist in the same orbit in an atom. E1E1 E2E2 E3E3 Allowed Not Allowed

Line Spectra Atomic Structure Electrons can move, as a result of energy inputs to the atom, to a higher energy orbit. In this case, the electron is said to be in an excited state. E1E1 E2E2 E3E3

Line Spectra Emission Spectrum In accordance with the Energy Minimum Principle, the electron will then “jump” to a lower energy state. In doing so, it will give up a specific amount of energy through the emission of a photon. E1E1 E2E2 E3E3 E 3 – E 2 = h f 32

Line Spectra Emission Spectrum It will continue to cascade down until it reaches the ground state. E1E1 E2E2 E3E3 E 2 – E 1 = h f 21

Line Spectra Emission Spectrum The electron can also bypass intermediate orbits. E1E1 E2E2 E3E3 E 3 – E 1 = h f 31

Line Spectra Emission Spectrum The atom will “glow” at frequencies determined by the difference in energy between the various orbits in the atom. E1E1 E2E2 E3E3

Line Spectra Hydrogen Spectrum E1E1 E2E2 E3E3 E4E4 All atoms have an infinite number of energy levels (orbits) The energy corresponding to the ground state is the lowest electron energy The energy corresponding to the first excited state is the second lowest energy. Etc

Line Spectra Hydrogen Spectrum E1E1 E2E2 E3E3 E4E4 The energy difference between orbits gets smaller and smaller as you go to higher and higher orbital energies.

Line Spectra Hydrogen Spectrum E1E1 E2E2 E3E3 E4E4 For hydrogen E n = eV n2n2 Therefore, the energy of emitted photons is E photon = 13.6 eV (1/n 2 – 1/p 2 ) n is the quantum number of the final orbit p is the quantum number of the starting orbit

Line Spectra Hydrogen Spectrum Note: Negative electron energy means that the electron is bound to the nucleus

Line Spectra Hydrogen Spectrum E photon = 13.6 eV ( 1/ /p 2 ) p = 2,3,4 … Lyman Series p = 3,4,5,… Balmer Series p = 4,5,6,.. Paschen Series E photon = hf = hc/λ E photon = 13.6 eV ( 1/ /p 2 ) E photon = 13.6 eV ( 1/ /p 2 )

Line Spectra Hydrogen Spectrum Ladder (Energy Level) Diagram Energy / / / /4 2 Ly α Ly γ Ly β Etc. Lyman series is Ultraviolet

Line Spectra Hydrogen Spectrum Ladder (Energy Level) Diagram Energy / / / /4 2 HαHα HγHγ HβHβ Etc. Balmer series is visible. Simply called the “H” lines rather than Balmer Lines

Line Spectra Hydrogen Spectrum Line λ (nm) Line Lyα 122UV HαHαHαHα656Visible Lyβ 103UV HβHβHβHβ486Visible Lyγ 97UV HγHγHγHγ434Visible

Line Spectra Hydrogen Spectrum

Line Spectra Hydrogen Spectrum HαHα HβHβ HγHγ Wavelength (nm) Intensity

Line spectra become VERY complicated as the number of electrons in orbit (and therefore the number of protons in the nucleus) grow Line Spectra Emission Spectrum of Neutral and Singly Ionized Iron