Concept explainers
Interpretation:
The forms of the five real
Concept introduction:
The wavefunction for
Where,
Answer to Problem 11.90E
The forms of the five real
Explanation of Solution
From Table 11.4, the equations used to determine five
Use Euler’s identity in the above wavefunctions as given below.
The imaginary part of wavefunctions with
The forms of the five real
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Chapter 11 Solutions
Physical Chemistry
- Verify that the wavefunctions in equation 10.20 satisfy the three-dimensional Schrdinger equation.arrow_forwardAn anharmonic oscillator has the potential function V=12kx2+cx4 where c can be considered a sort of anharmonicity constant. Determine the energy correction to the ground state of the anharmonic oscillator in terms of c, assuming that H is the ideal harmonic oscillator Hamiltonian operator. Use the integral table in Appendix 1 in this book.arrow_forwarda Construct Slater determinant wavefunctions for Be and B. Hint: Although you need only include one p orbital for B, you should recognize that up to six possible determinants can be constructed. b How many different Slater determinants can be constructed for C, assuming that the p electrons spread out among the available p orbitals and have the same spin? How many different Slater determinants are there for F?arrow_forward
- The OH bond in water vibrates at a frequency of 3650cm1. What wavelength and frequency in s1 of light would be required to change the vibrational quantum number from n=0 to n=4, assuming OH acts as a harmonic oscillator?arrow_forwardFor an unbound or free particle having mass m in the complete absence of any potential energy that is, V=0, the acceptable one-dimensional wavefunctions are =Aei(2mE)1/2x/h+Bei(2mE)1/2x/h, where A and B are constants and E is the energy of the particle. Is this wavefunction normalizable over the interval x+? Explain the significance of your answer.arrow_forwardInstead of x=0 to a, assume that the limits on the 1-D box were x=+(a/2) to (a/2). Derive acceptable wavefunction for this particle-in-a-box. You may have to consult an integral table to determine the normalization constant. What are the quantized energies for the particle?arrow_forward
- For the system in exercise 9.1, determine the Hamiltonian equation of motion.arrow_forwardUse the expression for 1 in equations 11.17 and normalize the wavefunction. Use the integral defined for the Hermite polynomials in Table 11.2. Compare your answer with the wavefunction defined by equation 11.19.arrow_forwardNormalize the following wavefunctions over the range indicated. You may have to use the integral table in Appendix 1. a =x,x=0to1b =x,x=0to2 c =sin2x,x=0tod =sin2x,x=0to2 e =sin3/2x,x=0to2arrow_forward
- a Assume that the electronic energy of Li was a product of three hydrogen-like wavefunctions with principal quantum number equal to 1. What would be the total energy of Li? b Assume that two of the principal quantum numbers are 1 and the third principal quantum number is 2. Calculate the estimated electronic energy. c Compare both energies with an experimental value of 3.261017J. Which estimate is better? Is there any reason you might assume that this estimate would be better from the start?arrow_forwardThe Balmer series is isolated from the other series of the hydrogen atom spectrum. This is not the case for all series. Determine the first value of n for which the hydrogen spectral series overlap.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,