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(1) (20 pts) Consider the {Mn2Ni3} system with spin Stot = 7...

(1) (20 pts) Consider the {Mn2Ni3} system with spin Stot = 7 described in the research article J. Am. Chem. Soc. 2011, 133, 3433. (a) Calculate the magnitude (in units of h) of spin angular momentum for Stot = 7. (Hint: Formula is similar to spin angular momentum of one electron. Make sure to use...

Question One. Answer all parts (i)-(vii) (i) A system con...

Question One. Answer all parts (i)-(vii) (i) A system contains 4 equivalent molecules (N=4). The molecules are distributed over a series of 4 energy levels labelled 1, 2, 3 and 4, having energies equal to 0, 8, 2e and 3e respectively. The total energy of the system is 7E. Any allowed configurat...

1) Do electrons really spin? Although electrons act as if th...

1) Do electrons really spin? Although electrons act as if they are "spinning" and they definitely have a magnetic dipole moment, they aren't actually tiny spinning objects. a) As a simple model for a spinning charged object, let' is consider a circular ring of charge with radius...

1. Distributions (A) Calculate the number of ways to divide...

1. Distributions (A) Calculate the number of ways to divide 17 distinguishable objects into 5 groups as follows: group A has 5 objects group B has 0 objects group C has 7 objects group D has 2 objects group E has 3 objects (B) Suppose you can’t evaluate factorials (x!) directly. Show m...

In this experiment we obtain the IR spectrum of HCl and DCl....

In this experiment we obtain the IR spectrum of HCl and DCl. Although these spectra are easily distinguished by the isotope of hydrogen, the chlorine isotopes make a much smaller difference. Each signal in the spectrum of HCl is actually two signals: one for H35Cl and another for H37Cl. Similarly...

Valence bond theory - hybrid orbitals Let’s consider ...

Valence bond theory - hybrid orbitals Let’s consider two hybrid orbitals: h3 = s – px + py – pz and h4 = s + px – py – pz. (a) Normalize the hybrid orbital h4. (b) Show that the hybrid orbitals h4 and h3 are orthogonal. (c) Argue for an angle between the hybrid orbi...

1. Rotational spectroscopy The line spacing for ³⁵Cl...

1. Rotational spectroscopy The line spacing for ³⁵Cl¹⁹F is 1.033 cm¯¹. Calculate the moment of inertia, the reduced mass, and the bond length for the molecule. 2. Vibrational spectroscopy A certain diatomic molecule yield a vibrational spectrum with the first four peaks ...

1. One mole of Ar(g) (assume a perfect gas) is expanded adia...

1. One mole of Ar(g) (assume a perfect gas) is expanded adiabatically with a constant number of moles. If the initial and final pressures are 1.000 × 105 Pa and 0.950 × 105 Pa, respectively and the initial temperature is 300.0 K, what is the final temperature? 2. Using the final tempe...

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