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Arrangement of Electrons in Atoms • Principles of electromagnetic radiation led to Bohr’s model of the atom. • Electron location is described using identification numbers called quantum numbers. • Rules for expressing electron location results in a unique electron configuration for each element. Mullis 1 Wave Description of Light • Electromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space • Wavelength (λ) – Distance between corresponding points on adjacent waves. – Unit: nm,cm,m • Frequency (ν) – Number of waves that pass a specific point in a given time – Unit: Hz or waves/sec Recall that Speed = Distance/time (m/sec) • Speed of light (c) C=λν Mullis 2 Behavior of Light • Photoelectric effect – The emission of electrons when light shines on the metal – Scientists found that below a certain frequency, no electrons were emitted. – Light also behaves as a particle: Since hot objects do not emit em energy continuously, they must emit energy in small chunks called quanta. • Quantum – Minimum quantity of energy that can be gained or lost by an atom Mullis 3 Light as a particle and a wave Planck and Einstein • Max Planck: Relationship between quantum of energy and wave frequency • Planck’s constant h = 6.626 x 10-34 J-s E = hν E is energy, ν is frequency • Albert Einstein: Established dual wave-particle nature of light 1st – Einstein explained PE effect by proposing that EM radiation is absorbed by matter only in whole numbers of photons. – Electron is knocked off metal surface only if struck by one photon with certain minimum energy. Mullis 4 Louis de Broglie • Because we know that light has a particle nature, we might ask if matter has wave nature. • Louis de Broglie answered this. His equation: λ = h/mv • Lambda is a wave property. • Momentum (mass x velocity) is a particle property. • In one equation, de Broglie summarized the concepts of waves and particles as they apply to high-speed, low mass objects. • Results of de Broglie’s discovery include X-ray diffraction and electron microscopy techniques used to study small objects. Mullis 5 Quantum Theory • Ground state: An atom’s lowest energy state • Excited state: Higher potential energy than ground state. • Photon: A particle of electromagnetic radiation having zero mass and carrying a quantum of energy (i.e., packet of light) • Only certain wavelengths of light are emitted by hydrogen atoms when electric current is passed through—Why? Mullis 6 Niels Bohr links hydrogen’s electron with photon emission • Bohr proposed that an electron circles the nucleus in allowed orbits at specific energy levels. – Lowest energy is close to nucleus • Bohr’s theory explained the spectral lines seen in hydrogen’s line emission spectrum, but it did not hold true for other elements. Mullis 7 Quantum Numbers • • • • Principal quantum number, n Angular momentum quantum number, l Magnetic quantum number, ml Spin quantum number, ms Mullis 8 Azimuthal quantum number = Angular momentum quantum number • Depends on the value of n • Values of l starts at 0 and increases to n-1 • This number defines the shape of the orbital. Orbital s p d f Mullis l 0 1 2 3 9 Magnetic quantum number • Magnetic quantum number is the orientation of an orbital around the nucleus. • It is the number of orbitals in a sublevel. Orbitals per sublevel The s sublevel has 1 orbital. The p sublevel has 3 orbitals. The d sublevel has 5 orbitals. The f sublevel has 7 orbitals. Mullis s p d f 1 3 5 7 10 Quantum numbers 1s ____ 2s ____ 2p ____ ____ ____ 3s _____ Principal quantum number Magnetic quantum number Angular momentum quantum number Mullis 11 Quantum numbers 1s ____ 2s ____ ms = -1/2 2p ____ ____ ____ ml = -1 3s _____ ml =0 ms = +1/2 ml = +1 Magnetic quantum number Principal quantum number Angular momentum quantum number [ for a p orbital, l = 1] Mullis 12 Magnetic quantum number, ml • Gives the 3d orientation of each orbital. • Has value from –l to + l • Example: 3p refers to orbitals with n = 3 and l = 1. Values of ml = -1,0,1 • These three numbers correspond the 3 possible orientations of the dumbbell-shaped p orbitals (x,y and z axis). Mullis 13