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#Chem 161-2007 Homework 9th week

#Chem 161-2007 Homework 9th week - Chem 161-2007 Homework...

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Chem 161-2007 Homework 9 th Week Hill & Petrucci Homework Chapter 7 & 8 Chapter 7 problems: 45,47,53,55,57,61,63,65,74,93 Chapter 8 problems: 3,21,25,27,31,37,75 The Bohr Model of the Hydrogen Atom 45. What is the energy of the photon emitted when the electron in a hydrogen atom drops from the energy level n=6 to the energy level (a) n = 1, and (b) n = 4? ∆E = -B((1/n f 2 ) – (1/n i 2 )) B = 2.179 x 10 -18 J (a) ∆E = (-2.179 x 10 -18 J)((1/(1) 2 ) – (1/(6) 2 )) = -2.12 x 10 -18 J; i.e., 2.12 x 10 -18 J emitted. (b) ∆E = (-2.179 x 10 -18 J)((1/(4) 2 ) – (1/(6) 2 )) = -0.076 x 10 -18 J; i.e., 0.076 x 10 -18 J emitted. 47. Calculate the frequency, in s -1 , of the electromagnetic radiation emitted by a hydrogen atom when its electron drops from (a) the n = 5 to the n = 2 energy level, and (b) from the n = 3 to the n = 1 energy level. ∆E = -B((1/n f 2 ) – (1/n i 2 )) E photon = h υ h υ = -B((1/n f 2 ) – (1/n i 2 )) υ = ((-B)((1/n f 2 ) – (1/n i 2 )))/(h) (a) υ = ((-2.179 x 10 -18 J) x ((1/(2) 2 ) – (1/(5) 2 )))/(6.626x10 -34 Js) = -6.91 x 10 14 J My answer to “a” is in disagreement with the Solutions Manual. I don’t know why. (b) υ = ((-2.179 x 10 -18 J) x ((1/(1) 2 ) – (1/(3) 2 )))/(6.626x10 -34 Js) = -29.2 x 10 14 J Matter as Waves 53. Calculate the wavelength, in nanometers, associated with a proton traveling at a speed of 1.96 x 10 5 ms -1 . Use 1.67 x 10 -27 kg as the proton mass. DeBroglie theorem: λ= h/mv λ= (6.626 x 10 -34 Js)/((1.67 x 10 -27 kg) x (1.96 x 10 5 ms -1 )) = 2.02 x 10 -12 m This answer is different than the Solutions Manual. The Solutions Manual has a typo, calling the speed 1.96 x 10 6 ms -1 . Self-Assessment Questions 55. Electrons from an electron microscope have an associated wavelength of 0.00510 nm. To what speed, in meters per second, are the electrons accelerated? λ= h/mv v = h/λm mass of one electron = 9.11 x 10 -31 kg v = (6.626 x 10 -34 Js)/((0.00510 nm) x (1x10 -9 m/nm) x (9.11 x 10 -31 kg)) = 1.43 x 10 8 m/s Quantum Numbers and Atomic Orbitals Chem 161-2007 homework 9 th week 1
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57. What is the lowest numbered principal shell in which (a) p orbitals are found, and (b) the f subshell can be found? From a graphical diagram, it can be seen that a p orbital is found in principal shells ≥2, and an f subshell is found in principal shells ≥4. 61. Indicate whether each of the following is a permissible set of quantum numbers. If the set is not permissible, state why it is not. (a) n = 2, l = 0, m l = +1 (b) n = 5, l = 3, m l = -3 (c) n = 4, l = 3, m l = -2 (d) n = 0, l = 0, m l = 0 (a) If n = 2, l = 0 to 2 – 1 = 0 to 1. Since l = 0, this is OK. If l = 0, m l = -0 to +0 = 0. Since m l = +1, this is not OK. (b) If n = 5, l = 0 to 5-1 = 0,1,2,3 or 4. Since l = 3, this is OK. If l = 3, m l = -3 to +3 = -3,-2,-1,0,+1,+2,+3. Since m l = -3, this is OK. (c) If n = 4, l = 0 to 4-1 = 0 to 3 = 0,1,2 or 3. Since l = 3, this is OK.
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