College Physics B - PHY2054C

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1 of College - PHY2054C The of 11/17/2014 My Office Hours: Tuesday 10:00 AM - Noon 206 Keen Building

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3 of Puzzling The blackbody intensity falls to zero at both long and short wavelengths, corresponding to low and high frequencies, with a peak in the middle at the location given by Wien s law. At that time, physicists knew that electromagnetic waves form standing waves. Waves on a string have frequencies following the pattern: f n = n f 1, n = 1, 2, 3,... In classical theory: No limit to the value of n. Ultraviolet Catastrophe In Mechanics: p photon = hf c = h λ

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5 Atomic Spectra of Helium

6 of Classical Atom Existence of spectral lines required new model of atom, so that only certain amounts of energy could be emitted or absorbed. By about 1890, most physicists and chemists believed matter was composed of atoms consisting of electrons and protons. The behavior could not be explained by Newton s mechanics. Plum Pudding Model

7 Scattering Experiments of Ernest Rutherford (30 August October 1937) Rutherford expected the relatively massive α particles would pass freely through the plum-pudding atom. A small number of alpha particles were actually deflected through very large angles.

8 of Review Question 1 According to the Rutherford experiment (and later model) of the atom, most of the volume of an atom: A is empty space. B was occupied by the nucleus. C contained positive charges. D excluded electrons.

9 of Review Question 1 According to the Rutherford experiment (and later model) of the atom, most of the volume of an atom: A is empty space. B was occupied by the nucleus. C contained positive charges. D excluded electrons.

10 of Planetary Model of Atom In Rutherford s Planetary Model, the electric force between the proton and the electron supplies a centripetal force: ke 2 v = rm KE = 1 2 mv 2 = 7.5 ev 13.6 ev Value is very close to the measured ionization energy of the hydrogen atom of 13.6 ev, but:

11 of Planetary Model of Atom In Rutherford s Planetary Model, the electric force between the proton and the electron supplies a centripetal force: ke 2 v = rm KE = 1 2 mv 2 = 7.5 ev 13.6 ev Value is very close to the measured ionization energy of the hydrogen atom of 13.6 ev, but:

12 of Bohr Model of Atom Existence of spectral lines required new model of atom, so that only certain amounts of energy could be emitted or absorbed. Bohr Model had certain allowed orbits for electron: (works nicely for atoms with one electron, e.g. H, He +, etc.)

13 of Modern Atom Emission energies correspond to energy differences between allowed levels. Modern Model has electron cloud rather than orbit:

14 of 1 In an atom, Atomic the negative electrons orbit the positive nucleus and form standing waves known as orbitals. Each orbital can have at most two electrons in it. (Pauli Exclusion Principle)

15 of 1 In an atom, Atomic the negative electrons orbit the positive nucleus and form standing waves known as orbitals. Each orbital can have at most two electrons in it. (Pauli Exclusion Principle) 3 D Standing Waves resemble the 2 D standing waves of the drumhead

16 of 1 In an atom, Atomic the negative electrons orbit the positive nucleus and form standing waves known as orbitals. Each orbital can have at most two electrons in it. 2 An orbital s energy = kinetic + potential The energy of a photon is: E photon = h f Since energy is conserved, the energy of the photon is the difference in energy of the atom before and after emission or absorption. 3 Electrons normally reside in the lowest energy orbitals Ground state 4 Electrons can be excited to higher energy orbitals.

17 of Wait a second: Why are electrons waves? Atomic

18 of Wait a second: Why are electrons waves? Atomic Wave-particle duality: Electrons have both particle and wave characteristics. Like all objects in the universe, electrons travel as waves when they move from place to place. It is only when you look for them that you find them as particles at particular locations.

19 of Wave Characteristics of Electrons Clinton J. Davisson ( ) Lester H. Germer ( ) Observed interference effects when electrons reflected from different atomic layers in crystal of nickel metal (1927). This is described by the Heisenberg Uncertainty Principle: x p h/4π

20 of Atomic Electrons reside in standing waves: An electron in an orbital does not emit light. An electron emits light when it changes orbitals.

21 of Atomic Electrons reside in standing waves: An electron in an orbital does not emit light. An electron emits light when it changes orbitals. Light travels as a wave (a diffuse pattern) is emitted or absorbed as a particle (a photon): Photon energy = Planck constant frequency E = h f An atom s orbitals differ by specific energies: Energy differences establish photon energies. Atom emits a specific spectrum of photons.

22 of Question 2 If a hydrogen atom, originally in its ground state of energy 13.6 ev, absorbs a photon of energy 16.0 ev, then what is the resulting kinetic energy of the electron if the proton has negligible kinetic energy? A Such a photon cannot be absorbed in this case. B 2.4 ev C 2.4 ev D 16.0 ev

23 of Question 2 If a hydrogen atom, originally in its ground state of energy 13.6 ev, absorbs a photon of energy 16.0 ev, then what is the resulting kinetic energy of the electron if the proton has negligible kinetic energy? A Such a photon cannot be absorbed in this case. B 2.4 ev C 2.4 ev D 16.0 ev

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25 Atomic Excitations of (a) Direct Decay (b) Cascades

26 of Absorption is created when atoms absorb photons of right energy for excitation. Multi-Electron Atoms have much more complicated spectra, many more possible states.

27 of Absorption is created when atoms absorb photons of right energy for excitation. Multi-Electron Atoms have much more complicated spectra, many more possible states. Helium Carbon

28 Hydrogen Spectra of Molecular Spectra are much more complex than atomic spectra, even for hydrogen: (a) Molecular Hydrogen (b) Atomic Hydrogen

29 of Question 3 When a wire carries high current causing it to glow, it will emit which type of spectrum? A Emission spectrum B Absorption spectrum C Continuous spectrum D Monochromatic spectrum

30 of Question 3 When a wire carries high current causing it to glow, it will emit which type of spectrum? A Emission spectrum B Absorption spectrum C Continuous spectrum ( ) D Monochromatic spectrum

31 of Question 4 When a high voltage is applied to a low-pressure gas causing it to glow, it will emit which type of spectrum? A Emission spectrum B Absorption spectrum C Continuous spectrum D Monochromatic spectrum

32 of Question 4 When a high voltage is applied to a low-pressure gas causing it to glow, it will emit which type of spectrum? A Emission spectrum B Absorption spectrum C Continuous spectrum D Monochromatic spectrum

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34 of 1 Principle Number n As n increases, the average distance from the electron to the nucleus increases. State with a particular value of n are referred to as a shell.

35 of 1 Principle Number n 2 Orbital Number l The angular momentum of the electron is proportional to l. States with l = 0 have no angular momentum. Spherical shape of orbital l = 0: s-orbital, l = 1: p-orbital, l = 2: d-orbital,...

36 of 1 Principle Number n 2 Orbital Number l 3 Orbital Magnetic Number m l You can think of m as giving the direction of the angular momentum of the electron in a particular state.

37 of 1 Principle Number n 2 Orbital Number l 3 Orbital Magnetic Number m l 4 Spin Number s Often referred to as spin up and spin down Gives the direction of electron s spin angular momentum.

38 of : Examples Electron configuration of the Hydrogen ground state: 1s 1 1 n = 1 2 The only allowed state for l is l = 0 (s state). 3 The only allowed state for m is m = 0. 4 The allowed states for s are s = ±1/2.

39 of : Examples Electron configuration of the Helium ground state: 1s 2 1 n = 1 2 The only allowed state for l is l = 0 (s state). 3 The only allowed state for m is m = 0. 4 The allowed states for s are s = ±1/2.

40 of : Examples Electron configuration of the Carbon ground state: 1s 2 2s 2 2p 2 1 n = 1, 2 2 The only allowed state for l is l = 0, 1 (s and p states). 3...