Consider the He atom, and assume that the two electrons reside in the 2s orbital. The...
Consider the He atom, and assume that the two electrons reside in the 2s orbital. The next two items refer to this situation.
- Ignoring electron-electron repulsion, what is the electronic energy of the atom (in eV)? Write down the corresponding electronic wavefunction.
- Use perturbation theory to account for electron-electron interaction and write down an expression for the electronic energy of this atom. No need to evaluate integrals, but specify coordinates, integration volume and limits of integration.
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Consider the He atom, and assume that the two electrons reside
in the 2s orbital. The...
3. In the ground electronic state of Li atom, the electron configuration is 1s 2s'. If...
3. In the ground electronic state of Li atom, the electron configuration is 1s 2s'. If we neglect all the electron-electron repulsion, and assume all Li atomic orbitals follow those in hydrogenic atoms. Determine the energy (in eV) of the electron ground state: 1s2 2s1. Namely, the total energy of the 3 electrons in 1s 2s'. Check the end of chapter problem: E8C.2(a). 3. In the ground electronic state of Li atom, the electron configuration is 1s 2s1. If we...
1. Consider the wavefunction of the 2s orbital of the hydrogen atom: -Dexp (-) where do...
1. Consider the wavefunction of the 2s orbital of the hydrogen atom: -Dexp (-) where do is the Bohr's radius (0.52918 nm). (25) = 42 (a) (15pt) Determine the expectation value of the potential < > of the 2s orbital in ev. (b) (10pt) Determine the expectation value of the kinetic energy of the 2s orbital in eV. (c) (5pt) Determine the location of the radial node (if there is any) in nm. (d) (5pt) Determine the location of the...
1: Part A: Two electrons occupy the 2s shell in a Be atom (Z = 4)....
1: Part A: Two electrons occupy the 2s shell in a Be atom (Z = 4). What are the possible quantum numbers J for the total angular momentum of this two-electron system, neglecting any contributions from the nucleus or 1s level? Part B: Calculate the energy required to cause an electron from the 2s shell to jump to each of the 2p, 3s, 3p, and 3d states. E1 for Be is 9.3 eV. En = (-Z2E1)/n2. One of the listed...
3. Knowing that the magnesium and aluminum atoms possesses 12 and 13 electrons respectively: (a) Write...
3. Knowing that the magnesium and aluminum atoms possesses 12 and 13 electrons respectively: (a) Write down the electron configuration (nl) of the ground state. Explain your answer. (b) We focus on the electron configuration determined in (a). Considering only the electrons from the outer subshell, add their electronic spins and their orbital angular momenta separately. Label the total spin and the total orbital momentum quantum numbers by s and l, respectively. Write down the possible values spanned by s...
3. Knowing that the magnesium and aluminum atoms possesses 12 and 13 electrons respectively: (a) Write...
3. Knowing that the magnesium and aluminum atoms possesses 12 and 13 electrons respectively: (a) Write down the electron configuration (nl) of the ground state. Explain your answer. (b) We focus on the electron configuration determined in (a). Considering only the electrons from the outer subshell, add their electronic spins and their orbital angular momenta separately. Label the total spin and the total orbital momentum quantum numbers by s and l, respectively. Write down the possible values spanned by s...
Simple molecular orbital theory for the ethylene molecule. (a) (5 points) Write down a Hamiltonian matrix for the pi electrons of ethylene, using a 2p basis function on each C atom, and assuming that...
Simple molecular orbital theory for the ethylene
molecule.
(a) (5 points) Write down a Hamiltonian matrix for the pi electrons of ethylene, using a 2p basis function on each C atom, and assuming that the matrix elements of the Hamiltonian are α for on-site interaction you a 2 by 2 matrix - it is known as the Huckel Hamiltonian s, and B for the interactions between nearest neighbors This should give (b) (10 points) Write down the secular equation for...
Effective Nuclear Charge and Periodic Trends Coulombs Law describes the interaction between two charges and varies...
Effective Nuclear Charge and Periodic Trends Coulombs Law describes the interaction between two charges and varies by the magnitude of these charges and inversely with the distance between them. ? ∝ ?1?2/? For atoms, we’ll label the charges as the nuclear charge and electron charge. ? ∝ ?????????/? As you go up in atomic number (Z), the number of protons in the nucleus increases, making the charge on the nucleus increase, so that in general. ???? = ? ∙ (+1)...
(5 pts] Saraw orbital diagrams for atoms with the following electron configurations:15 2s 2p 3s 3p...
(5 pts] Saraw orbital diagrams for atoms with the following electron configurations:15 2s 2p 3s 3p 45-30 33. Write the equations representing the following processes. In each case, be sure to indicate the physical state of the ions. [2 x 4 pts) The electron affinity of S (1) The fourth ionization energy of titanium (TI) 34 For each of the following pairs, indicate which one of the two species is larger: (3 x 1 pt) (a) N or F- (b)...
(5 pts] Saraw orbital diagrams for atoms with the following electron configurations:15 2s 2p 3s 3p 45-30 33. Write t...
(5 pts] Saraw orbital diagrams for atoms with the following electron configurations:15 2s 2p 3s 3p 45-30 33. Write the equations representing the following processes. In each case, be sure to indicate the physical state of the ions. [2 x 4 pts) The electron affinity of S (1) The fourth ionization energy of titanium (TI) 34 For each of the following pairs, indicate which one of the two species is larger: (3 x 1 pt) (a) N or F- (b)...
#2 This is a solid state physics problem. ( I use this book : kittel introduction...
#2
This is a solid state physics problem. ( I use this book : kittel
introduction to soild state physocs ) thank you !
5. [Graphene] Consider graphene, a hexagonal lattice of carbon atoms as shown in the figure. The distance between neighboring carbon atoms is a0.143 nm (a) B A (a) Write down the unit lattice vectors ā, and a and unit reciprocal lattice vectors b, and b,. [5] a2 (b) The two sites A and B are not...
3. In the ground electronic state of Li atom, the electron configuration is 1s 2s'. If we neglect all the electron-electron repulsion, and assume all Li atomic orbitals follow those in hydrogenic atoms. Determine the energy (in eV) of the electron ground state: 1s2 2s1. Namely, the total energy of the 3 electrons in 1s 2s'. Check the end of chapter problem: E8C.2(a). 3. In the ground electronic state of Li atom, the electron configuration is 1s 2s1. If we...
1. Consider the wavefunction of the 2s orbital of the hydrogen atom: -Dexp (-) where do is the Bohr's radius (0.52918 nm). (25) = 42 (a) (15pt) Determine the expectation value of the potential < > of the 2s orbital in ev. (b) (10pt) Determine the expectation value of the kinetic energy of the 2s orbital in eV. (c) (5pt) Determine the location of the radial node (if there is any) in nm. (d) (5pt) Determine the location of the...
Simple molecular orbital theory for the ethylene
molecule.
(a) (5 points) Write down a Hamiltonian matrix for the pi electrons of ethylene, using a 2p basis function on each C atom, and assuming that the matrix elements of the Hamiltonian are α for on-site interaction you a 2 by 2 matrix - it is known as the Huckel Hamiltonian s, and B for the interactions between nearest neighbors This should give (b) (10 points) Write down the secular equation for...
(5 pts] Saraw orbital diagrams for atoms with the following electron configurations:15 2s 2p 3s 3p 45-30 33. Write the equations representing the following processes. In each case, be sure to indicate the physical state of the ions. [2 x 4 pts) The electron affinity of S (1) The fourth ionization energy of titanium (TI) 34 For each of the following pairs, indicate which one of the two species is larger: (3 x 1 pt) (a) N or F- (b)...
(5 pts] Saraw orbital diagrams for atoms with the following electron configurations:15 2s 2p 3s 3p 45-30 33. Write the equations representing the following processes. In each case, be sure to indicate the physical state of the ions. [2 x 4 pts) The electron affinity of S (1) The fourth ionization energy of titanium (TI) 34 For each of the following pairs, indicate which one of the two species is larger: (3 x 1 pt) (a) N or F- (b)...
#2
This is a solid state physics problem. ( I use this book : kittel
introduction to soild state physocs ) thank you !
5. [Graphene] Consider graphene, a hexagonal lattice of carbon atoms as shown in the figure. The distance between neighboring carbon atoms is a0.143 nm (a) B A (a) Write down the unit lattice vectors ā, and a and unit reciprocal lattice vectors b, and b,. [5] a2 (b) The two sites A and B are not...
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