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In: Chemistry

What is the ground electronic configuration of phosphorous? How many microstates does this configuration contain? Write...

What is the ground electronic configuration of phosphorous? How many microstates does this configuration contain? Write the spin arrow diagram for phosphorus. Derive the term and state symbols. How many microstates does each state contain? Which state is the ground state?

Solutions

Expert Solution

Ans- atomic number of phosphorous is 15

15P= 1s2 2s2 2p6 3s2 3p3 (electronic configuration)

For p3 : L = 0, S = 3/2, the term 4 S has J = 3/2 only (|L+S| = |L–S|). Therefore, the ground state is 4 S3/2.

, For a p3 configuration there are three terms: 4 S, 2 D, and 2 P. The J values for each of these are determined below. For 4 S: L = 0, S = 3/2 ; Because J = L + S, L + S – 1, …|L – S|, the quantum number J can only be 3/2 and there is a single state for 4 S: 4 S3/2 For 2 D: L = 2, S = 1/2. Possible J values are 5/2 and 3/2, and the two possible states are 2 D5/2 and 2 D3/2. For 2 P: L = 1, S = 1/2. Possible J values are 3/2 and 1/2, with states 2 P3/2 and 2 P1/2. The lowest energy state is 4 S3/2 (highest multiplicity). 2 D5/2 and 2 D3/2 are next, at 19233.18 and 19224.46 cm–1, and 2 P3/2 and 2 P1/2 are the highest energy at 28838.92 and 28839.31 cm–1.


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