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Why are lithium and beryllium so conductive? The $2s$ band has a much different energy range from the $2p$ band, so I guess the only explanation is that $N$ states are empty. But if that was the case, why isn't chlorine also a amazing conductor, since chlorine has $N$ empty states as well in the valence band?

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    $\begingroup$ For lithium, like any alkali metal, the $nS$ band is only half filled, making it automatically a conductor. $\endgroup$
    – Buzz
    Commented Dec 17, 2023 at 3:29
  • $\begingroup$ By following the same reasoning Cl should be a great conductor too or S which has 2N empty states(Li only has N empty states) $\endgroup$ Commented Dec 17, 2023 at 3:30
  • $\begingroup$ I don't know what you mean by $N$ here. In any case, there is a big difference in practice between group I and group VII elements, because the principal quantum number of the outer orbitals remain constant along each period, but the nuclear charge increases (decreasing the atomic radius and increasing their electronegativity). $\endgroup$
    – Buzz
    Commented Dec 17, 2023 at 3:34
  • $\begingroup$ $N$states . The $2s$ energy band of $N$ molecules has $2N$ states and since the $2s$ orbital of $Li$ is half filled we have $N$ occupied states and $N$ free states. $\endgroup$ Commented Dec 17, 2023 at 3:37
  • $\begingroup$ @Buzz what does electronegativity have to do with anything?] $\endgroup$ Commented Dec 17, 2023 at 4:54

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I'm not sure if you are thinking of comparing the three substances at normal temperature and pressure (NTP) or you want to think of chlorine as a solid. I'll go through both.

At NTP chlorine is a gas. All gases at NTP are expected to be good insulators (at normal voltages) because of the distance between the particles. Electrons won't flow, so to say.

As a solid, chlorine can be pictured as Cl2 molecules held together by weak forces. Because of the molecular nature, you should look to the molecular orbital diagram. In a Cl2 MO diagram, all electrons are paired, so in the solid a filled band is a possibility if no other band overlaps it. Because the molecules are bound weakly and the layers are far apart, one would expect a small perturbation to the MO picture. With no other MOs nearby in energy to form overlapping bands, one expects to have a filled band and thus an insulator.

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  • $\begingroup$ How does chlorine not having empty states since the atom Chlorine needs 1 additional electron to fully fill its orbitals? $\endgroup$ Commented Dec 19, 2023 at 11:19
  • $\begingroup$ I'm not sure what you are saying before the word "since". But, I get the feel for what you are asking. Chlorine does not naturally exist as lone atoms. It is diatomic: Cl2. If you look up the octet rule in a high school chemistry text, you'll see the details. The octet rule is just a rule of thumb, but you should start your understanding there. The lone electrons in each of the two Cl atoms come together to form a covalent bond. $\endgroup$
    – Dr. Nate
    Commented Dec 19, 2023 at 17:09
  • $\begingroup$ So what? A CL2 molecules has still 2 empty states in its antibonding molecular orbital. A Cl(N) molecule has 2N empty states. $\endgroup$ Commented Dec 19, 2023 at 17:21
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    $\begingroup$ When the Cl2 molecules solidify into a periodic solid, the MO will hybridize into electronic bands. But, because these are minimally perturbed Cl2 molecules, the hybridization is weak. This cause the bands to not be wide. The energy width of the HOMO and LUMO bands are not high enough to cross the energy difference between these HOMO and LUMO levels. That is to say, they don't overlap. So, there is a filled band and unfilled band, which means there is no conduction. $\endgroup$
    – Dr. Nate
    Commented Dec 19, 2023 at 17:34
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The conductivity of a material depends on several factors, such as the number of valence electrons, the band structure, the crystal structure, the temperature, and the presence of impurities.

Lithium and beryllium are metals with one and two valence electrons, respectively. They have a simple hexagonal crystal structure that allows their electrons to form overlapping bands. This means that there is no band gap between the 2s and 2p orbitals, and the electrons can move freely across both bands. Therefore, lithium and beryllium have high conductivity.

Chlorine is a nonmetal with seven valence electrons. It has a complex orthorhombic crystal structure that creates a large band gap between the 3s and 3p orbitals. This means that the electrons are confined to their respective orbitals and cannot move across the band gap. Therefore, chlorine has low conductivity.

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  • $\begingroup$ The 2s energy band has very different energy range from the 2p energy band tho.It shouldnt be close. $\endgroup$ Commented Dec 17, 2023 at 5:22
  • $\begingroup$ "Chlorine is a nonmetal with seven valence electrons. It has a complex orthorhombic crystal structure that creates a large band gap between the 3s and 3p orbitals.".You mean the 3p and 4s? $\endgroup$ Commented Dec 17, 2023 at 5:23
  • $\begingroup$ Actually, the 2s and 2p energy bands are not very different in energy. They are separated by Lamb shift, which is due to quantum electrodynamics effects. Therefore, the 2s and 2p orbitals can be considered as having the same energy for most purposes. Regarding chlorine, No, I mean the 3s and 3p orbitals. The 4s orbital is empty and has a higher energy than the 3p orbital. Therefore, the band gap is between the 3s and 3p orbitals, not the 3p and 4s orbitals. @RootGroves $\endgroup$
    – Titan78
    Commented Dec 18, 2023 at 8:35
  • $\begingroup$ Hi Titan, your first para is okay. The situation is complex. Your second and third paras are lacking. In your 2nd para, you make it seem like hexagonal structure alone with no consideration of the atomic basis or lattice spacing can determine the band structure. Your 3rd para does that again but also ignores the pairing from molecular orbitals. $\endgroup$
    – Dr. Nate
    Commented Dec 18, 2023 at 14:18
  • $\begingroup$ @Titan78 sorry not be rude I am trying to learn new thing but from what I have learnt so far your answer makes no sense.The next available energy band is the 4s band. $\endgroup$ Commented Dec 19, 2023 at 15:25

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