Show that a variation theory treatment of
Interpretation:
The variation theory treatment of
Concept introduction:
According to the variation theory, the lower the energy of a system the better is the approximation. Variation theory is based on the fact that any test system has average energy equal to or greater than the ground state energy of that system. The advantage of the variation theory is that any wavefunction can be taken for any test system.
Answer to Problem 12.44E
The variation theory treatment of
Explanation of Solution
The expression for trial function can be written as given below.
Substitute the values in the above expression as follows.
The above equation can be simplified as given below.
Solve the integral as follows.
The value of
Substitute this value in the expression for trial energy as given below.
The exact energy of hydrogen atom in ground state is given by the expression written below.
From the above equation it is clear that the exact energy of hydrogen atom in ground state is same as the minimized trial energy.
The variation theory treatment of
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Chapter 12 Solutions
EBK PHYSICAL CHEMISTRY
- The particle in a box (PiB) model can be applied to electrons which move freely in a molecule such as π electrons. 1,3-butadiene CH2=CH-CH=CH2 has an absorption peak in the UV-Vis spectrum at 290 nm. This peaks is assigned to the π → π* transition of the lowest energy. This transition is also called the HOMO → LUMO transition. As a simple approximation, let’s consider molecule of butadiene as being potential 1D box of length 3 * 1.4 Å = 4.2 Å, when counting three carbon-carbon bonds each 1.4 Å long. Also let’s consider the four π electrons occupy molecular orbitals MOs and energy of MOs is calculated according to the PiB model. a) Sketch the scheme of MOs of butadiene molecule and populate them with electrons. b) Calculate the wavelength of light λcalc which corresponds to absorption of light and excitation of π electron from the HOMO to the LUMO in the molecule of butadiene. c) Compare this calculated λcalc with experimental value of λexp = 290 nm provided above, and explain the…arrow_forwardArsenic, with configuration 3p³, has the term symbols 2p, 2D, 4S. Find the possible J values for each of these, and match the appropriate set of J values with each term symbol. C. 2p E. 2D B. A. B. 4S 1123 312 c. 112 D. 112 512 312 E. 1/2. 312 512 ?arrow_forwardP19.11 Show that the selection rule for the two-dimensional rotor in the dipole approximation is Am₁ = ±1. Use A+em and A'+eim₂ for the initial and final states of the rotor and ucos as the dipole moment element.arrow_forward
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- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,