5. Consider the following two hybrid orbitals: ϕa = N (2pz + γ2s), ϕb = N (2s - γ2pz) where 2p and 2s are atomic orbitals on one atom. (a) Determine the normalization constant N, expressed in terms of...
5. Consider the following two hybrid orbitals: ϕa = N (2pz + γ2s), ϕb = N (2s - γ2pz) where 2p and 2s are atomic orbitals on one atom. (a) Determine the normalization constant N, expressed in terms of the constant γ. (b) Show that ϕa and ϕb are orthogonal. (c) Sketch the shape of these hybrid orbitals for γ ≒ 0.2. (d) Repeat part (c) for γ = 1.0.
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5. Consider the following two hybrid orbitals: ϕa = N (2pz + γ2s), ϕb = N (2s - γ2pz) where 2p and 2s are atomic orbitals on one atom. (a) Determine the normalization constant N, expressed in terms of...
Please show all work. Use the following two equations to determine the orthonormal hybrid orbitals 0.45...
Please show all work.
Use the following two equations to determine the orthonormal
hybrid orbitals
0.45 2s 0.71 2p,+0.55 2p = =0.45- 2s - 0.71 - 2p, +0.55 2p Use the coordinate system shown below for a water molecule. Show that we can write the two bonding hybrid atomic orbitals on the oxygen atom as h-NNT 2S(sin0) 2p, + (cose)2p.) and b2 = N(y2s-(sin0) 2py+ (cos0)2p.) where y is constant and N is the normalization constant. Now use the fact...
Consider the sp, sp2, and sp3 hybrid orbitals. Use the general orbital form ϕ = N (2p + γ2s) and cos θ = - γ2. Calculate the value of γ for each of these types of hybrid orbitals. What is the percent...
Consider the sp, sp2, and sp3 hybrid orbitals. Use the general orbital form ϕ = N (2p + γ2s) and cos θ = - γ2. Calculate the value of γ for each of these types of hybrid orbitals. What is the percent contribution of the 2s atomic orbital to each of these types of hybrid orbitals? help
3) Rank the following orbitals in order of increasing energy: 3s, 2s, 2p, 4s, 3p, ls,...
3) Rank the following orbitals in order of increasing energy: 3s, 2s, 2p, 4s, 3p, ls, and 3d. 4) How many orbitals in an atom can have the following quantum number or designation? a. 3p_ b. 7s c. 4p. d. 5d . e. 5f f. n=5 5) Answer the following questions by filling in the space: a) The quantum number n describes the of an atomic orbital. b) The shape of an atomic orbital is given by the quantum number...
Consider an H2+ ion. In the figure below, HẠ, HB, and e represent the two nuclei...
Consider an H2+ ion. In the figure below, HẠ, HB, and e represent the two nuclei and the electron, respectively, and all the relevant distances are defined. You must use atomic units for this problem. (a) (4 points) Write down the Born-Oppenheimer Hamiltonian for the H2+ ion. R HA H (b) (6 points) The anti-bonding molecular orbital is expressed as V = N_(ls (r) – 1s (r)), where ls, (r) and 1s; (r) are hydrogen Is orbitals centered at nuclei...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can'...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
Please show all work.
Use the following two equations to determine the orthonormal
hybrid orbitals
0.45 2s 0.71 2p,+0.55 2p = =0.45- 2s - 0.71 - 2p, +0.55 2p Use the coordinate system shown below for a water molecule. Show that we can write the two bonding hybrid atomic orbitals on the oxygen atom as h-NNT 2S(sin0) 2p, + (cose)2p.) and b2 = N(y2s-(sin0) 2py+ (cos0)2p.) where y is constant and N is the normalization constant. Now use the fact...
3) Rank the following orbitals in order of increasing energy: 3s, 2s, 2p, 4s, 3p, ls, and 3d. 4) How many orbitals in an atom can have the following quantum number or designation? a. 3p_ b. 7s c. 4p. d. 5d . e. 5f f. n=5 5) Answer the following questions by filling in the space: a) The quantum number n describes the of an atomic orbital. b) The shape of an atomic orbital is given by the quantum number...
Consider an H2+ ion. In the figure below, HẠ, HB, and e represent the two nuclei and the electron, respectively, and all the relevant distances are defined. You must use atomic units for this problem. (a) (4 points) Write down the Born-Oppenheimer Hamiltonian for the H2+ ion. R HA H (b) (6 points) The anti-bonding molecular orbital is expressed as V = N_(ls (r) – 1s (r)), where ls, (r) and 1s; (r) are hydrogen Is orbitals centered at nuclei...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
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