Chem 161-2008 Homework 8th week

Chem 161-2008 Homework 8th week - Chem 161-2008 Homework...

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Chem 161-2008 Homework 8 th Week Hill & Petrucci Homework Chapter 7 Chem 161-2008 Hill & Petrucci Chapter 7 Homework Chapter 7 problems: 5,23,27,29,31,35,37,41,45,47,53,69,74,89,90,97 Self-Assessment Questions 5. Which property of waves is not mathematically related to the other three? (a) wavelength (b) frequency (c) speed (d) amplitude In the equations below, wavelength of light is related to the frequency and speed of light, frequency of light is related to the wavelength and speed of light, and speed of light is related to the wavelength and frequency of light. None of these parameters is related to amplitude. Amplitude is the intensity of light, which is related to the number of atoms or molecules undergoing the transition. E photon = hυ υ = c/λ E = hc/λ Subatomic Particles 23. The mass-to-charge ratio of the proton is 1.044 x 10 -8 kg/C. What is the charge on a proton? What is its mass? The charge on a proton is +1. Since, according to Millikan, the charge on one proton is 1.602 x 10 -19 coulomb, then: 1.044 x 10 -8 kg/C x (1.602 x 10 -19 coulomb/proton) = 1.67 x 10 -27 kg/proton. 27. Determine appropriate mass-to-charge ratios for the following ions. (a) 80 Br - (b) 18 O 2- (c) 40 Ar + Why are these values only approximate? (Hint: What are the masses of these ions?) Note to students: Look at “b” for a thorough explanation. (a) The mass-to-charge ratio is 80:1. We don’t have to write this in SI units, because that wasn’t requested. However, the Solutions Manual wrote the answer in SI units. Writing this in SI units, as kg Br atom/Coulomb, and considering that there are 1.602x10 -19 C/electron charge: (80g x (1kg/1000g)/(6.022x10 23 ))/(1.602x10 -19 C) = 8.29x10 -7 kg/C (b) It seems to me that an acceptable answer should be that the mass-to-charge ratio is 18:2 = 9:1, i.e., the mass of a particular isotope of oxygen divided by the charge. However, the convention for most problems in the quantum mechanics area is to deal with atoms (not moles) and SI units, i.e., kg (not grams). In addition, although you and I would refer to the charge as “-2” or “2-“, the official unit of charge is “Coulombs”, in which the charge of one electron is 1.602 x 10 -19 Coulombs. In summary, divide the mass (in kg) of 1 atom of the substance by the number of coulombs. 1

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(18 g/mol x (1 mol/(6.022 x 10 23 atoms)) x (1 kg/1000g))/(2 electrons x 1.602 x 10 -19 coulombs/electron) = 9.33x10 -8 kg/C (c) The mass-to-charge ratio is 40:1. (40g x (1kg/1000g)/(6.022x10 23 ))/(1.602x10 -19 C) = 4.15x10 -7 kg/C These values are only approximate because the atomic mass numbers is an approximation of the mass of the ion, not exactly the mass of the ion.
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