# Chapter 6 - Electronic Structure of Atoms - Additional Exercises: 6.102f

The condensed electron configuration of $Sg$ is $$Sg:[Rn]5f^{14}6d^{4}7s^2$$ There are 4 unpaired electrons.

#### Work Step by Step

1) The nearest noble gas of lower atomic number of $Sg$ is $Rn$. 2) Looking the periodic table, the atomic number of $Sg$ is 106, which means it has 106 electrons. The last row ends with the atomic number 86, so $Sg$ has 86 inner-shell electrons. That leaves it with 20 outer-shell electrons. $Sg$ belongs to the 7th row, so its outer shell is the 7th shell. 3) These 20 outer-shell electrons are distributed as follows: - The first two go to the $7s$ subshell. - The next 14 go to the $5f$ subshell. - The last 4 go to the $6d$ subshell. Therefore, the condensed electron configuration of $Sg$ is $$Sg:[Rn]5f^{14}6d^{4}7s^2$$ 4) All the inner shells, the $7s$ subshell, the $5f$ subshell are completely filled, so all of their electrons are paired. There are 4 electrons in subshell $6d$, and subshell $6d$ has 5 orbitals. According to Hund's rule, these 4 electrons each occupies a different orbital. In the end, there are 4 one-electron orbitals. Therefore, there are 4 unpaired electrons.

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