Key Equations. Determining the smallest change in an atom's energy.
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1 ATOMIC STRUCTURE AND PERIODICITY Matter and Energy Key Equations λν = c ΔE = hν Relating speed of a wave to its wavelength and frequency. Determining the smallest change in an atom's energy. H( λ =R n in E= B ( Z n final ) n out Predicting the position and wavelength of any line in the H atom spectrum (Rydberg equation). Z ) n initial Finding the difference between two energy levels in the H atom (Bohr model). λ = h/mv x (mv h ) 4 π Calculating the wavelength of any moving particle (de Broglie wavelength). Finding the uncertainty in position or in momentum of a particle (Heisenberg uncertainty principle).. Your favourite FM station broadcast at a frequency of. MHz. What is the wavelength of this radiation?. Calculate the frequency of a red light of wavelength.5 x nm.. Sodium atoms have a characteristic yellow color when excited in a flame. The color comes from the emission of light of 589. nm. (a) What is the frequency of this radiation? (b) What is the change in energy associated with this photon? (c) per mole of photon? 4. It takes 8 kj of energy to remove one mole of electrons from gaseous cesium. What is the wavelength associated with this energy? 5. Calculate the energy change corresponding to the excitation of an electron from n = to n = electronic state in hydrogen atom. What wavelength of electromagnetic radiation is associated with this energy change Page
2 . Calculate the wavelength for an electron (mass = 9. x kg) travelling at a speed of. x 7 m/s and for a ball (. kg) travelling at 5 m/s. 7. An electron (9. x kg) and a 5. g baseball are each travelling at m/s. Calculate the uncertainty in position of each. The Quantum-Mechanical Model of the Atom Quantum numbers Quantum Number Information Allowed Values principal quantum number (n) size and energy of orbital n =,,,... angular momentum quantum number (l) shape l = to n magnetic quantum number (m l ) orientation of orbital in space m l = l to l, including electron spin quantum number (m s ) orientation of the spin m s = +½ or ½ Shell, n Subshell, l (name) Allowed combinations of the n, l, m l, and m s quantum numbers m l Number of orbitals m s e capacity subshell shell 4l + n (s) (s) (p),, + 8 (s) (p) (d),, +,,, +, (4s) (4p) (4d) (4f),, +,,, +, +,,,, +, +, Page
3 Shapes of orbitals s orbital, l = p orbital, l = d orbital, l = 8. Give the name, the m l s and the number of orbitals for each subshell with the given quantum numbers. (a) n =, l = (c) n = 5, l = (b) n =, l = (d) n = 4, l = 9. How many electrons can each of the following subshells hold? (a) s (d) d (b) 5p (e) 4d (d) 4f (f) p x. Which of the following sets of quantum numbers are allowed or not allowed? If not, why? (a) n =, l =, m l =, m s (b) n = 4, l =, m l =, m s (c) n = 4, l =, m l =, m s = +½ (d) n =, l =, m l =, m s = (e) n = 5, l = 4, m l =, m s = +½ (f) n =, l =, m l =, m s (g) n =, l =, m l =, m s = Electron Configuration Aufbau Principle Pauli Exclusion Principle Hund s Rule Add one electron per element to the lowest energy orbital available. No two electrons in an atom may have identical sets of four quantum numbers. Electrons occupy all the orbitals of a given subshell singly before pairing begins. These unpaired electrons have parallel spins. Page
4 . Write the electron configuration for: (a) boron (b) sulphur (c) iodine. Give the number of valence electrons in: (a) boron (b) sulphur (c) iodine Draw orbital diagrams for: (a) sodium (b) phosphorous 4 Write the electron configuration for: (a) Li + (b) Br (c) Se Periodic Trends in Atomic Properties 5. Order the atoms from smallest to largest radius: Cs, Si, F, Ca, Ga. Order the following from smallest to largest radius: Mg, Al, Ca 7. In each of the following sets, which atom or ion has the smallest radius? (a) Li, Na, K (b) P, As (c) O +, O, O (d) S, Cl, Kr (e) Pd, Ni, Cu 8. Order the following from smallest to largest radius: O, Na +, F, Mg + and Al + Page 4
5 9. In each of the following sets, which atom or ion has the smallest ionization energy? (a) Ca, Sr, Ba (b) K, Mn, Ga (c) N, O, F (d) S, S, S + (e) Cs, Ge, Ar. The first ionization energies of As and Se are.947 and.94 MJ/mol, respectively. Rationalize these s in terms of electron configuration.. The electron affinities of the elements from aluminium to chlorine are 44,, 74,.4 and 84.7 kj/mol, respectively. Rationalize the trend in these s.. Order the atoms in each of the following sets from least exothermic EA to the most. (a) S, Se (b) Cl, Br, I (c) N, O, F (d) Al, Si, P Page 5
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