(4) Thermodynamic data suggests that copper monohalides (CuX) should exist as polymers in the gas...
(4) Thermodynamic data suggests that copper monohalides (CuX) should exist as polymers in the gas phaso However, scientists have successfully synthesized CuX monomers and characterized them using microwave spectroscopy For Cu Br the J-13 14,J-1415 and J-1516 transitions occurred at 84421.34 MHz, 90449.25 MHz and 96476.72 MHz, respectively. Assuming Cu Br behaves as a 3D rigid rotor, answer the following questions. Note: Absorption frequency (in units of Hz) of a rotational transition (aka peak position in a microwave spectrum) corresponding to Δ,-±l is given as: ˇ-2BU + 1) where B-8 Here B is called as the rotational constant of the molecule and J represents the angular momentum quantum number of the initial eigenstate. (a) Calculate the rotational constant (in Hz). (Hint: Think if using peak position itself or if using difference between peak positions would yield more "accurate" value for B.) (b) Using your answer for #(a) calculate the moment of-inertia (in kg-m2). (c) Using your answer for #(b) calculate the bond length (in m) (Atomic masses are 63Cu-629296 amu and Br 78.9183 amu). (d) How well does your value in #(c) agree with the experimental bond length of 2.1734x 10-10 m? in your opinion, is 3D rigid rotor model a valid one to describe the rotational transitions in 6Cu Br? Briefly explain your reasoning. (e) Do you expect the bond length to be different or same for Cu" Br, "Cu'Br and Cu"Br? Briefly explain your reasoning. hcz2 Roo ing questions use the energy expression in hydrogenic atoms which is given as En- rt (5) Determine the ratio of the ground state energy of atomic hydrogen to that of atomic deuterium. (6) Virial theorem states that "in a system of multi-particles (such as nuclei and electrons) the average total kinetic energy Coulomb forces are acting on each other." Using Schrödinger wavefunctions of hydrogenic systems it can mathematically be proven that for a 2s electron in hydrogen atom (V) 2(E). T) and the average total potential energy V) satisfy the relation 2(T) +(V)-0 when the (a) Evaluate (V) for a 2s electron in a hydrogen atom. (b) Now, use your result from (a) & the Virial theorem stated above to calculate the average kinetic energy of a 2s electron in a hydrogen atom.
(4) Thermodynamic data suggests that copper monohalides (CuX) should exist as polymers in the gas phaso However, scientists have successfully synthesized CuX monomers and characterized them using microwave spectroscopy For Cu Br the J-13 14,J-1415 and J-1516 transitions occurred at 84421.34 MHz, 90449.25 MHz and 96476.72 MHz, respectively. Assuming Cu Br behaves as a 3D rigid rotor, answer the following questions. Note: Absorption frequency (in units of Hz) of a rotational transition (aka peak position in a microwave spectrum) corresponding to Δ,-±l is given as: ˇ-2BU + 1) where B-8 Here B is called as the rotational constant of the molecule and J represents the angular momentum quantum number of the initial eigenstate. (a) Calculate the rotational constant (in Hz). (Hint: Think if using peak position itself or if using difference between peak positions would yield more "accurate" value for B.) (b) Using your answer for #(a) calculate the moment of-inertia (in kg-m2). (c) Using your answer for #(b) calculate the bond length (in m) (Atomic masses are 63Cu-629296 amu and Br 78.9183 amu). (d) How well does your value in #(c) agree with the experimental bond length of 2.1734x 10-10 m? in your opinion, is 3D rigid rotor model a valid one to describe the rotational transitions in 6Cu Br? Briefly explain your reasoning. (e) Do you expect the bond length to be different or same for Cu" Br, "Cu'Br and Cu"Br? Briefly explain your reasoning. hcz2 Roo ing questions use the energy expression in hydrogenic atoms which is given as En- rt (5) Determine the ratio of the ground state energy of atomic hydrogen to that of atomic deuterium. (6) Virial theorem states that "in a system of multi-particles (such as nuclei and electrons) the average total kinetic energy Coulomb forces are acting on each other." Using Schrödinger wavefunctions of hydrogenic systems it can mathematically be proven that for a 2s electron in hydrogen atom (V) 2(E). T) and the average total potential energy V) satisfy the relation 2(T) +(V)-0 when the (a) Evaluate (V) for a 2s electron in a hydrogen atom. (b) Now, use your result from (a) & the Virial theorem stated above to calculate the average kinetic energy of a 2s electron in a hydrogen atom.