Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 42.2, Problem 42.2QQ
To determine
Whether the statement is true or false.
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To give a helium atom nonzero angular momentum requires about 21.2 eV of energy (that is, 21.2 eV is the difference between the energies of the lowest-energy or ground state and the lowest-energy state with angular momentum). The electron-volt or eV is defined as 1.60 × 10−19 J. Find the temperature T where this amount of energy equals kB T/2. Does this explain why we can ignore the rotational energy of helium for most purposes? (The results for other monatomic gases, and for diatomic gases rotating around the axis connecting the two atoms, have comparable orders of magnitude.)
Let's consider the three atoms composing the molecule now have different masses and coordinate, while the axis of rotation is still z axis that is perpendicular to the xy plane. The first atom has a mass of 142.54 kg, with x coordinate at 3 m and y coordinate at 6 m. The second atom has a mass of 82.55 kg, with x coordinate at 1 m and y coordinate at 6 m. The third atom has a mass of 8 kg, with x coordinate at 5 m and y coordinate at 9 m. What is the moment of inertia in unit of kg m2 with respect to the x axis?
Consider two immiscible liquids such as water and oil. If a spherical oil molecule of radius r is taken out of the oil phase and placed in the water phase, the unfavorable energy of this transfer is proportional to the area of the solute (oil) molecule newly exposed to the solvent (water) multiplied by the interfacial energy, i, of the oil-water interface. The interfacial energy of the bulk cyclohexane-water interface is i = 50 mJ m-2, and the radius of a cyclohexane molecule is 0.28 nm. Using Boltzmann distribution, estimate the solubility of cyclohexane in water at 25 C in units of mol L-1.The concentration of water in water phase is 55.5 mol L-1.
Chapter 42 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 42.1 - For each of the following atoms or molecules,...Ch. 42.2 - Prob. 42.2QQCh. 42.2 - Prob. 42.3QQCh. 42 - Prob. 1PCh. 42 - Prob. 2PCh. 42 - Prob. 3PCh. 42 - Prob. 4PCh. 42 - Prob. 5PCh. 42 - The photon frequency that would be absorbed by the...Ch. 42 - Prob. 8P
Ch. 42 - Prob. 9PCh. 42 - Prob. 10PCh. 42 - (a) In an HCl molecule, take the Cl atom to be the...Ch. 42 - Prob. 12PCh. 42 - Prob. 13PCh. 42 - Prob. 14PCh. 42 - Prob. 15PCh. 42 - Prob. 16PCh. 42 - Prob. 17PCh. 42 - Prob. 19PCh. 42 - Prob. 21PCh. 42 - Prob. 22PCh. 42 - Prob. 23PCh. 42 - Prob. 24PCh. 42 - Prob. 25PCh. 42 - Prob. 26PCh. 42 - Prob. 27PCh. 42 - Prob. 28PCh. 42 - Prob. 29PCh. 42 - Prob. 30PCh. 42 - Prob. 32PCh. 42 - Prob. 33PCh. 42 - Prob. 35PCh. 42 - Prob. 36APCh. 42 - Prob. 37APCh. 42 - Prob. 39APCh. 42 - Prob. 40APCh. 42 - As an alternative to Equation 42.1, another useful...
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- The v = 0 to v = 1 vibrational transition of the HI molecule occurs at a frequency of 6.69 × 1013 Hz. The same transition for the NO molecule occurs at a frequency of 5.63 × 1013 Hz. Calculate (a) the effective force constant and (b) the amplitude of vibration for each molecule. (c) Explain why the force constant of the NO molecule is so much larger than that of the HI molecule.arrow_forwardConsider a gas in a cubical container 22 cm on a side. How many states lie within ±0.01% of the momentum magnitude p=1.6×10−23 kg⋅m/s (a plausible momentum for a nitrogen molecule in a gas at room temperature)? The number of states that lie within ±0.01% of the momentum magnitude p=1.6×10−23 kg⋅m/s is × ______10^25.arrow_forwardAlthough an ordinary H2 molecule consists of two identical atoms, this is not the case for the molecule HD, with one atom of deuterium (Le., heavy hydrogen, 2H). Because of its small moment of inertia, the HD molecule has a relatively large value of E: 0.0057 eV. At approximately what temperature would you expect the rotational heat capacity of a gas of HD molecules to "freeze out," that is, to fall significantly below the constant value predicted by the equipartition theorem?arrow_forward
- (a) In an HCl molecule, take the Cl atom to be the isotope 35Cl. The equilibrium separation of the H and Cl atoms is 0.127 46 nm. The atomic mass of the H atom is 1.007 825 u and that of the 35Cl atom is 34.968 853 u. Calculate the longest wavelength in the rotational spectrum of this molecule. (b) What If? Repeat the calculation in part (a), but take the Cl atom to be the isotope 37Cl, which has atomic mass 36.965 903 u. The equilibrium separation distance is the same as in part (a). (c) Naturally occurring chlorine contains approximately three parts of 35Cl to one part of 37Cl. Because of the two different Cl masses, each line in the microwave rotational spectrum of HCl is split into a doublet as shown in Figure P42.11. Calculate the separation in wavelength between the doublet lines for the longest wavelength.arrow_forwardThe active element of a certain laser is made of a glass rod 30.0 cm long and 1.50 cm in diameter. Assume the average coefficient of linear expansion of the glass is equal to 9.00 106 (C)1. If the temperature of the rod increases by 65.0C, what is the increase in (a) its length, (b) its diameter, and (c) its volume?arrow_forwardA rigid tank of volume V = 0.014 m3 contains carbon monoxide at a temperature of T0 = 25° C and a pressure of P0 = 9.00 × 105 Pa. This molecule should be treated as a diatomic ideal gas with active vibrational modes. Part (a) In this model, how many degrees of freedom does each molecule of carbon monoxide have? Part (b) The temperature of the gas increases by 10° C. Select the process that has occurred from the choices below. Part (c) Calculate the pressure of the gas in pascal at this increased temperature. Part (d) Calculate the change to the internal energy of the gas in joules. Part (e) Calculate the change in the entropy of the gas in joules per kelvin. I know you cannot answer all parts however manyuo can will helparrow_forward
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