PHYSICAL CHEMISTRY-STUDENT SOLN.MAN.
2nd Edition
ISBN: 9781285074788
Author: Ball
Publisher: CENGAGE L
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Chapter 10, Problem 10.91E
Interpretation Introduction
Interpretation:
The value of
Concept introduction:
In
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The J = 0 to J = 1 rotational transition of the CO molecule occurs at a frequency of 1.15 x 1011 Hz.(A) Use this information to calculate the moment of inertia of the molecule. (B) Calculate the bond length of the molecule.
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Chapter 10 Solutions
PHYSICAL CHEMISTRY-STUDENT SOLN.MAN.
Ch. 10 - State the postulates of quantum mechanics...Ch. 10 - Prob. 10.2ECh. 10 - State whether the following functions are...Ch. 10 - State whether the following functions are...Ch. 10 - Prob. 10.5ECh. 10 - Prob. 10.6ECh. 10 - Evaluate the operations in parts a, b, and f in...Ch. 10 - The following operators and functions are defined:...Ch. 10 - Prob. 10.9ECh. 10 - Indicate which of these expressions yield...
Ch. 10 - Indicate which of these expressions yield an...Ch. 10 - Why is multiplying a function by a constant...Ch. 10 - Prob. 10.13ECh. 10 - Using the original definition of the momentum...Ch. 10 - Under what conditions would the operator described...Ch. 10 - A particle on a ring has a wavefunction =12eim...Ch. 10 - Calculate the uncertainty in position, x, of a...Ch. 10 - For an atom of mercury, an electron in the 1s...Ch. 10 - Classically, a hydrogen atom behaves as if it were...Ch. 10 - The largest known atom, francium, has an atomic...Ch. 10 - How is the Bohr theory of the hydrogen atom...Ch. 10 - Though not strictly equivalent, there is a similar...Ch. 10 - The uncertainty principle is related to the order...Ch. 10 - Prob. 10.24ECh. 10 - Prob. 10.25ECh. 10 - For a particle in a state having the wavefunction...Ch. 10 - Prob. 10.27ECh. 10 - A particle on a ring has a wavefunction =eim,...Ch. 10 - Prob. 10.29ECh. 10 - Prob. 10.30ECh. 10 - Prob. 10.31ECh. 10 - Normalize the following wavefunctions over the...Ch. 10 - Prob. 10.33ECh. 10 - Prob. 10.34ECh. 10 - For an unbound or free particle having mass m in...Ch. 10 - Prob. 10.36ECh. 10 - Prob. 10.37ECh. 10 - Prob. 10.38ECh. 10 - Evaluate the expression for the total energies for...Ch. 10 - Prob. 10.40ECh. 10 - Verify that the following wavefunctions are indeed...Ch. 10 - In exercise 10.41a, the wavefunction is not...Ch. 10 - Prob. 10.43ECh. 10 - Prob. 10.44ECh. 10 - Explain why n=0 is not allowed for a...Ch. 10 - Prob. 10.46ECh. 10 - Prob. 10.47ECh. 10 - Prob. 10.48ECh. 10 - Carotenes are molecules with alternating CC and...Ch. 10 - The electronic spectrum of the molecule butadiene,...Ch. 10 - Prob. 10.51ECh. 10 - Prob. 10.52ECh. 10 - Show that the normalization constants for the...Ch. 10 - Prob. 10.54ECh. 10 - Prob. 10.55ECh. 10 - An official baseball has a mass of 145g. a...Ch. 10 - Is the uncertainty principle consistent with our...Ch. 10 - Prob. 10.58ECh. 10 - Prob. 10.59ECh. 10 - Instead of x=0 to a, assume that the limits on the...Ch. 10 - In a plot of ||2, the maximum maxima in the plot...Ch. 10 - Prob. 10.62ECh. 10 - Prob. 10.63ECh. 10 - The average value of radius in a circular system,...Ch. 10 - Prob. 10.65ECh. 10 - Prob. 10.66ECh. 10 - Prob. 10.67ECh. 10 - Prob. 10.68ECh. 10 - Prob. 10.69ECh. 10 - Assume that for a particle on a ring the operator...Ch. 10 - Mathematically, the uncertainty A in some...Ch. 10 - Prob. 10.72ECh. 10 - Prob. 10.73ECh. 10 - Verify that the wavefunctions in equation 10.20...Ch. 10 - An electron is confined to a box of dimensions...Ch. 10 - a What is the ratio of energy levels having the...Ch. 10 - Consider a one-dimensional particle-in-a-box and a...Ch. 10 - Prob. 10.78ECh. 10 - Prob. 10.79ECh. 10 - Prob. 10.80ECh. 10 - Prob. 10.81ECh. 10 - What are x,y, and z for 111 of a 3-D...Ch. 10 - Prob. 10.83ECh. 10 - Prob. 10.84ECh. 10 - Prob. 10.85ECh. 10 - Prob. 10.86ECh. 10 - Prob. 10.87ECh. 10 - Prob. 10.88ECh. 10 - Substitute (x,t)=eiEt/(x) into the time-dependent...Ch. 10 - Write (x,t)=eiEt/(x) in terms of sine and cosine,...Ch. 10 - Prob. 10.91ECh. 10 - Prob. 10.92ECh. 10 - Prob. 10.93ECh. 10 - Prob. 10.95E
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Similar questions
- Calculate the rotational energy of CO at J=2 given a bond length of 1.0 Å. unit in eV.arrow_forward(c) When a gas is expanded very rapidly, its temperature can fall to a few degrees Kelvin. At these low temperatures, unusual molecules like ArHCl (Argon weakly bonded to HCl) can form on mixing. For the isotopic species Ar H$CI, the following rotational transitions were observed: J (1 → 2): 6714.44 MHz J (2 → 3): 10068.90 MHz Assume the molecule can be treated as a linear diatomic molecule (ArCl). (i) Calculate the rotational constant (B) and centrifugal distortion (D) constant for this molecule.arrow_forwardConsider the diatomic molecule AB modeled as a rigid rotor (two masses separated by a fixed distance equal to the bond length of the molecule). The rotational constant of the diatomic AB is 25.5263 cm-1. (a) What is the difference in energy, expressed in wavenumbers, between the energy levels of AB with J = 10 and J = 6? (b) Consider now a diatomic A'B', for which the atomic masses are ma 0.85 mA and mB' 0.85 mB and for its bond length ra'B' = 0.913 rAB. What is the difference in energy, expressed in wavenumbers, between the energy levels of the A'B' molecule with J = 9 and J = 7?arrow_forward
- Rotational spectra are affected slightly by the fact that different isotopes have different masses. Suppose a sample of the common isotope 1H35Cl is changed to 1H37Cl. (a) By what fraction is the molecule’s rotational inertia different? (The bond length is 0.127 nm in each case.) (b) What is the change in energy of theℓ = 1 to theℓ = 0 transition if the isotope is changed?arrow_forwardJ.G. Dojahn et al. (J. Phys. Chem. 100, 9649 (1996)) characterized the potential energy curves of the ground and electronic states of homonuclear diatomic halogen anions. These anions have a 2Σu+ ground state and 2Πg, 2Πu, and 2Σg+ excited states. To which of the excited states are electric-dipole transitions allowed from the ground state? Explain your conclusion.arrow_forwardEvaluate Δx = (⟨x2⟩ − ⟨x⟩2)1/2 and Δpx = (⟨px2⟩ − ⟨px⟩2)1/2 for the ground state of (a) a particle in a box of length L and (b) a harmonic oscillator. Discuss these quantities with reference to the uncertainty principle.arrow_forward
- We can use the classical harmonic oscillator to think about molecular bonds. The HCI molecule has a force constant k = 481 N/m. For the mass, use the reduced mass, which is defined as µ = (m₁m₂)/(m₁+m₂). a) Plot the potential energy of HCl from -1 to 1 Å. What happens to the curvature of the potential as the force constant is varied? What does this mean physically? b) Plot position as a function of time for a total energy of 6 x 10-20 J. What is the period of the motion? How does the period change as the force constant is varied? Explain why this makes sense physically.arrow_forwardIdentify the systems for which it is essential to include a factor of 1/N! on going from Q to q : (i) a sample of helium gas, (ii) a sample of carbon monoxide gas, (iii) a solid sample of carbon monoxide, (iv) water vapour.arrow_forwardSince we will be dealing with partial derivatives later in the semester, this is a good opportunity to review this topic (see appendix C). Then evaluate the following partial derivatives (a) PV = nRT; (∂ P/∂V)T (b) r = (x2 + y2 + z 2 )1/2; (∂ r/∂y)x,zarrow_forward
- Consider the rotational temperatures of the following hetero diatomic molecules: θr(CO) = 2.1 K, θr(HF) = 30.2 K. In which case would the classical approximation be accurate? Justify your answer.arrow_forwardConsider a rotating molecule of ©Li'H. At T = 300 K, the rotational kinetic energy in the eighth excited state is equivalent to kgT, where kB is the Boltzmann constant. What is the energy of the first excited state relative to the ground state?arrow_forward. Suppose a system of 4 molecules has a total energy of Etot = 4(+) where the energy of each molecule can be in the range Co. Co+c, co + 2e, co + 3c, co + 4e. Find all possible configurations, calculate the weight of each, identify most probable configuration, and calculate the probability of observing the o state.arrow_forward
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