Physical Chemistry II:
Show that the transition J = 0 to J = 2 is not
allowed for rotational transitions in a diatomic molecule. The wave
functions are the appropriate spherical harmonics
YJ,m. Choose m=0. Remember that the dipole
moment is a vector that can be written 
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Physical Chemistry II:
Show that the transition J = 0 to J = 2 is not...
Suppose that the wavenumber of the J = 1 ← 0 rotational transition of 1H79Br considered...
Suppose that the wavenumber of the J = 1 ← 0 rotational transition of 1H79Br considered as a rigid rotor was measured to be 17.89 cm-1, what is (a) the moment of inertia of the molecule? Ans = _____ kg-m2 (b) the bond length? Ans = _____ Angstroms (Given the isotopic masses:(m(79Br) = 78.9183 amu, m(81Br) = 80.9163 amu)
5. A diatomic molecule (like H2) can be modeled as two atoms of equal mass m,...
5. A diatomic molecule (like H2) can be modeled as two atoms of equal mass m, connected by a rigid massless rod of length a. The system is free to rotate in 3-D. I claim the moment of inertia of this molecule around its ceater of mass is a. (Feel free to convince yourself that factor of k is coect!) Big hint if you 're having trouble getting started: this problem is directly related to McIntyre's Ch A) The energy...
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in...
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in the spherical coordinate representation is where ao-top- 0.5298 10-10rn is the Bohr radius, and μ is the electon-proton reduced mass. Here, the square of the angular momentum operator L2 in the spherical coordinate representation is given by: 2 (2.2) sin θー sin θ 00 The form of the Schrödinger equation means that all energy eigenstates separate into radial and angular motion, and we can write...
3 Angular Momentum and Spherical Harmonics For a quantum mechanical system that is able to rotate...
3 Angular Momentum and Spherical Harmonics For a quantum mechanical system that is able to rotate in 3D, one can always define a set of angular momentum operators J. Jy, J., often collectively written as a vector J. They must satisfy the commutation relations (, ] = ihſ, , Îu] = ihſ, J., ſu] = ihỈy. (1) In a more condensed notation, we may write [1,1]] = Žiheikh, i, j= 1,2,3 k=1 Here we've used the Levi-Civita symbol, defined as...
electromegnatic 22.2 EXERCISES 2-1 Show that 22-8) and (22-9) can also be -6 how that, in a li from (22-4) and (22-5) rather where P-0 and J,- Maxwell's equations first. be found completely fr...
electromegnatic 22.2
EXERCISES 2-1 Show that 22-8) and (22-9) can also be -6 how that, in a li from (22-4) and (22-5) rather where P-0 and J,- Maxwell's equations first. be found completely fro and n by starting (22-4 an by going back to equation frst. t, if the free charge and current is, φ-, const. (zero is 1 equations determine N position and time, 227 Consider a re distributions and the polarization and ma gnetiza- tion are all given...
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2...
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2 dx 2x+1 хр '(x’+x+3) f. I sin (2x) dx g. cos (3x) dx h. ſ(cos(2x)+ + secº (x))dx i. [V2x+1 dx j. S x(x² + 1) dx k. | xe m. [sec? (10x) dx 16 n. .si dx 1+x 0. 16x 1 + x dx 5 P. STA dx 9. [sec xV1 + tan x dx 14. Given f(x)=5e* - 4 and f(0) =...
5. A diatomic molecule (like H2) can be modeled as two atoms of equal mass m, connected by a rigid massless rod of length a. The system is free to rotate in 3-D. I claim the moment of inertia of this molecule around its ceater of mass is a. (Feel free to convince yourself that factor of k is coect!) Big hint if you 're having trouble getting started: this problem is directly related to McIntyre's Ch A) The energy...
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in the spherical coordinate representation is where ao-top- 0.5298 10-10rn is the Bohr radius, and μ is the electon-proton reduced mass. Here, the square of the angular momentum operator L2 in the spherical coordinate representation is given by: 2 (2.2) sin θー sin θ 00 The form of the Schrödinger equation means that all energy eigenstates separate into radial and angular motion, and we can write...
3 Angular Momentum and Spherical Harmonics For a quantum mechanical system that is able to rotate in 3D, one can always define a set of angular momentum operators J. Jy, J., often collectively written as a vector J. They must satisfy the commutation relations (, ] = ihſ, , Îu] = ihſ, J., ſu] = ihỈy. (1) In a more condensed notation, we may write [1,1]] = Žiheikh, i, j= 1,2,3 k=1 Here we've used the Levi-Civita symbol, defined as...
electromegnatic 22.2
EXERCISES 2-1 Show that 22-8) and (22-9) can also be -6 how that, in a li from (22-4) and (22-5) rather where P-0 and J,- Maxwell's equations first. be found completely fro and n by starting (22-4 an by going back to equation frst. t, if the free charge and current is, φ-, const. (zero is 1 equations determine N position and time, 227 Consider a re distributions and the polarization and ma gnetiza- tion are all given...
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2 dx 2x+1 хр '(x’+x+3) f. I sin (2x) dx g. cos (3x) dx h. ſ(cos(2x)+ + secº (x))dx i. [V2x+1 dx j. S x(x² + 1) dx k. | xe m. [sec? (10x) dx 16 n. .si dx 1+x 0. 16x 1 + x dx 5 P. STA dx 9. [sec xV1 + tan x dx 14. Given f(x)=5e* - 4 and f(0) =...
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