Assigments (Chapter 7): Atomic Structure 7.1 The brilliant red colors seen in fireworks are due to the emission of light with wavelengths around 650 nm when strontium salts such as Sr(NO3)2 and SrCO3 are heated (This can be easily demonstrated in the lab by dissolving one of these salts in methanol that contains a little water and igniting the mixture in an evaporating dish.) Calculate the frequency of red light of wavelength 6.50 x102 nm 7.2 Light near the middle of the ultraviolet region of the electromagnetic radiation spectrum has a frequency of 2.73 x 1016 s-1 Yellow light near the middle of the visible region of the spec- trum has a frequency of 5.26 x1014 s-1 Calculate the wavelength that corresponds to each of these two frequencies of light 7.3 In Exercise 7.2 we calculated the wavelengths of ultraviolet light of frequency 2.73 x 1016 s-1 and of yellow light of frequency 5.26 x 1014 s-1 Calculate the energy, in joules, of an individual photon of each Compare these photons by calculating the ratio of their energies 7.4 A green line of wavelength 4.86 x10-7m is observed in the emission spectrum of hydrogen Calculate the energy of one photon of this green light 7.5 (a) Calculate the wavelength in meters of an electron traveling at 1.24 x 107 m/s The mass of an electron is 9.11 x10-28 g (b) Calculate the wavelength of a baseball of mass 5.25 oz traveling at 92.5 mph Recall that J = kg.m2/s2 7.6 Write an acceptable set of four quantum numbers for each electron in a nitrogen atom 7.7 Write an acceptable set of four quantum numbers for each electron in a chlorine atom 7.8 The energy (in joules) of an electron energy level in the Bohr atom is given by the expression: En = -2.179 x 10-18 J/n2, where n is the quantum number that specifies the energy level What is the frequency in Hz of the radiation emitted when an electron falls from level n = to level n = 2? Nguyen Tien Thao, Faculty of Chemistry, Hanoi College of Science, VNU 19 -Le Thanh Tong, Hanoi, Vietnam Email: nguyentienthao@gmail.com 7.9 What are the allowed values of the magnetic quantum number ml associated with the l = sublevel? 7.10 If the quantum number n equals 4, what are the allowed values of l, associated with this value of n? 11 Which of the following are not acceptable sets of quantum numbers? a n = 4, l = 0, ml = c n = 0, l = 1, ml= b n = 2, l = 1, ml = -2 d n = 1, l = 0, ml= 7.12 Which of the following are not acceptable sets of quantum numbers? a n = 3, l = 1, ml= -1 c n = 2, l = 2, ml = b n = 7, l= 3, ml = +3 d n = 5, l = 1, ml = 7.13 Using only the periodic table, rank each set of main-group elements in order of decreasing atomic size: a) Ca, Mg, Sr (b) K, Ga, Ca (c) Br, Rb, Kr (d) Sr, Ca, Rb 7.14 Rank each set of ions in order of decreasing size, and explain your ranking: (a) Ca2+, Sr2+, Mg2+ (b) K+, S2-, Cl(c) Au+, Au3+ 7.15 Arrange each set in order of increasing atomic size: (a) Rb, K, Cs (b) C, O, Be (c) CI, K, S (d) Mg, K, Ca 7.16 How many electrons in an atom can have each of the following quantum number or sublevel designations? (a) 4p (b) n = 3, = ml = +1 (c) n = 5, l = Chemistry, Seventh Edition Steven S Zumdahl University of Illinois Susan A Zumdahl University of Illinois Chapter 7+ 8, Exercises: 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 89, 81, 83, 85, 87, 89 Nguyen Tien Thao, Faculty of Chemistry, Hanoi College of Science, VNU 19 -Le Thanh Tong, Hanoi, Vietnam Email: nguyentienthao@gmail.com For talented students in Honor Program 1.The wave function for the 2pz orbital in hydrogen atom is: \2 p Z ( ) / Ve V / cosT 2S ao z where ao is the value for the radius of the first Bohr orbital in meters (5.29 x10-11 m), V is Z(r/ao), r is the value for the distance from the nucleus in meters, and T is an angle Calculate the value of \ p z at r = ao for T = 0o (z axis) and for T = 90o (xy plan) For hydrogen atoms, the wave function for the state n =3, l = 0, ml = is \ 300 1 ( ) / (27 17V 2V )e V / 81 3S ao where ao is the value for the radius of the first Bohr orbital in meters (5.29 x10-11 m), V = r/ao Calculate th position of the nodes for this wave function One of the emission for spectral lines for Be3+ has a wavelenth of 254.4 nm for an electronic transition that begins in the state with n = What is the principle quantum number of lower-energy state corresponding to this emission? A certain microwave oven delivers 75.0 watts (J/s) of power to a coffee cup containing 50.0 g of water at 25.0oC If the wavelength of microwaves in the oven is 9.75 cm, how long does it take, and how many photons must be adsorbed, to make the water boil? The specific heat capacity of water is 4.19 J/K.g Assume only the water absorbs the energy of the microwaves When the excited electron in a hydrogen atom falls from n = to n = 4, a photon of blue light is emitted If an excited electron in He+ falls from n = 4, which energy level must it fall to so that a similar blue light (as with the hydrogen) is emitted Prove it Nguyen Tien Thao, Faculty of Chemistry, Hanoi College of Science, VNU 19 -Le Thanh Tong, Hanoi, Vietnam Email: nguyentienthao@gmail.com