Please answer all parts of the Problem 10.4 (A, B, and C). Show your work and la

Question

Please answer all parts of the Problem 10.4 (A, B, and C). Show your work and label the solutions, thanks!

10.4 Fermions and bosons As we have seen, the usual chemist's language that two electrons sharing an orbital (spatial state) have "opposite spins" is sloppy. The two electrons are in the spin singlet state, which is not the same as the m = 0 spin triplet state. (a) If two electrons are in the spin triplet state, one is in the Vioo spatial state, and one is in the 200 spatial state, write the spatial part of their joint wavefunction.

Explanation / Answer

In this solution, psi is denoted as p:

Since the electrons are fermions, so the wave function will be antisymmetric

(a) the joint asymmetric wave function for p100 and p200 will be

pA = 1/(2)1/2 [ p100(1) p200(2) - p200(1) p100(2)] where 1 and 2 are the states occupied by the particles and since the fermions are indistinguishable, it will be difficult to distinguish the particles in the system, therefore, we take two cases as shown above.

(b) For l = 1, there are ml = 2l + 1 = 2 x1 + 1 = 3, 3p orbitals with the values of ml = -1, 0 , +1, each orbitals have 2 electrons and therefore, the p subshell have 6 electrons which can fit into the big atom.

(c) For spin 1, spin quantum number s = n/2, so if spin s = 1 that means n = 2 and if s = 1, then ms = 2s + 1 = 2 x 1+ 1 = 3 , so there can be a maximum 3 electrons for this spin in an orbital, by pauli's exclusion principle, not two electrons can occupy the same subshell in an orbital.  

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