(a)
Why the ratio of the number of molecules in the
(b)
(i)
The ratio
(ii)
The ratio
(iii)
The ratio
(iv)
The ratio
(v)
The ratio
(c)
The reason why the ratio
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Mastering Physics with Pearson eText -- Standalone Access Card -- for University Physics with Modern Physics (14th Edition)
- (a) Repeat Exercise 31.2, and convert the energy to joules or calories. (b) If all of this energy is converted to thermal energy in the gas, what is its temperature increase, assuming 50.0 cm3 of ideal gas at 0.250atm pressure? (The small answer is consistent with the fact that the energy is large on a quantum mechanical scale but small on a macroscopic scale.)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_forward(b) Calculate the half width in nanometers for Doppler broadening of the 4s S 4p transition for atomic nickel at 361.939 nm (3619.39 Å) at a temperature of 20,000 K in both wavelength and frequency units. (e) Calculate the speed that an iron atom undergoing the 4s S 4p transition at 385.9911 nm (3859.911 Å) would have if the resulting line appeared at the rest wavelength for the same transition in nickel. (f) Compute the fraction of a sample of iron atoms at 10,000 K that would have the velocity calculatedin (e). (g) Create a spreadsheet to calculate the Doppler half width DlD in nanometers for the nickel and iron lines cited in (b) and (e) from 3000–10,000 K. (h) Consult the paper by Gornushkin et al. (note 10) and list the four sources of pressure broadening that they describe. Explain in detail how two of these sources originate in sample atoms.arrow_forward
- P2D.8 Use the fact that (∂U/∂V)T = a/Vm2for a van der Waals gas (Topic 1C)to show that μCp,m ≈ (2a/RT) − b by using the definition of μ and appropriaterelations between partial derivatives. Hint: Use the approximation pVm ≈ RTwhen it is justifiable to do so.arrow_forwardWhat is the probability that an O2 molecule in a sampleof oxygen at 300 K has a speed between 5.00 × 102 and5.10 × 102 m s-1 ? (Hint: Try approximating the area underthe Maxwell–Boltzmann distribution by small rectangles.)arrow_forwardFor a sample of helium, the hard sphere radius is 257 pm, the mean speed of atoms is 1200 m s-1, the mean free path is 480 Å and the collisional frequency for a single atom is 4.16x10(10) s. Calculate the root mean square displacement in m for the helium atoms after 10 minutes.arrow_forward
- Suppose an argon atom (atomic mass = 39.95 u) near the surface of the Earth where the temperature is 295 K is moving straight up with a speed that is equal to the root mean square speed. Assume that the atom does not collide with any other atom or molecules. To what height will the atom go up before it comes to rest? (Assume that the acceleration due to gravity remains constant.)arrow_forwardTo 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.)arrow_forwardThe molar polarization of fluorobenzene vapour varies linearly with T−1, and is 70.62 cm3 mol−1 at 351.0 K and 62.47 cm3 mol−1 at 423.2 K. Calculate the polarizability and dipole moment of the molecule.arrow_forward
- A molecule in Earth's atmosphere at 20 °C has a most probable energy E = kT/2 = 2.02 ×10-21 J E = kT =4.04 ×10-21 J E = 3 k T / 2 = 6.1 ×10-21 J that depends on the mass of the moleculearrow_forwardCalculate (a) the thermal wavelength, (b) the translational partition function of an Ar atom in a cubic box of side 1.00 cm at (i) 300 K and (ii) 3000 K.arrow_forward
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