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![Prove the following identities.
(a) [t, p²] = 2ihp
(b) [p, ²] = -2ihâ](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5bf4ba0-b032-4556-ac45-0f5d16670fd8%2F480ad50b-d12f-4439-b246-b466cbf003e0%2Fhzjdp9s_processed.jpeg&w=3840&q=75)
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- Calculate the size of the quantum involved in the excitation of an electronic motion of frequency 1.0 x 1015 Hz. Ans: 400 kJ/molVanadium tetrachloride (VCl4 ) is a bright red colored liquid with a vapor pressure of 5x10-2 torr at 298K. What is the expected orbital angular momentum in the ground state of VCl4(g) ?Discuss how to derive diatomic term symbols e.g N2 and what do the + and - signs over terms mean.
- A space probe was designed to see 13CO in the atmosphere of Saturn by looking for lines in its rotational spectrum. If the bond length of CO is 112.8 pm, at what wave number do the first three rotational transitions appear?Would the light from fireflies be considered an example of a fluorescence or a phosphorescence process?What configurations must undergo the distortions predicted by the Jahn-Teller theorem? Why is distortion at eg level greater than at t2g?
- To what speed must a proton be accelerated from rest for it to have a de Broglie wavelength of 100 pm? What accelerating potential difference is needed?The moment of inertia of CH4 can be calculated from the expression I=8/3 mHR2 where R is the C-H bond length (109 angstrom or 109 x 1012 m). a. What is the lowest possible rotational energy of the CH4 molecule and what is the value of quantum number l associated with that rotational energy? b. Calculate the rotational energy of the molecule in the first excited state (when quantum number l = 1). c. Determine the degeneracy of the first excited state. Explain what is meant by rotational energy degeneracy.1)What is the value of the Langmuir constant "a"? 2)What is the value of the Langmuir constant "b"?
- Calculate the rotational energy of CO at J=2 given a bond length of 1.0 Å. unit in eV.7.5 B What must the distance be between charges of +2.25 and −1.86 for the attractive force between them to be the same as that between charges of +4.06 and −2.11 separated by a distance of 2.16 pm?(a) Express the moment of inertia of an octahedral AB6 molecule in terms of its bond lengths and the masses of the B atoms. (b) Calculate the rotational constant of 32S19F6 , for which the S—F bond length is 158 pm.