# I Electron bands in solids

#### cube137

With regards to the number of states available to the electrons in these solids.

1. a mass of polycrystalline iron (plenty of free electrons)
2. quartz (has practically no free electrons).
3. semiconductors

Which of them has the most number of states available to the electrons?
Which has the most ease of getting them to change states considered against the ease with which they change states by themselves?

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#### cube137

To rephrase it. An electron in isolation has discrete value. When it is part of solid, The formerly discrete nature of allowed energies for an electron is turned into thick energy bands, within which electrons can occupy any energy they desire (well, almost). In this sense, you have many states available to the electrons.

Which of these... iron, quartz or semiconductors have most states available to the electrons?

What other solid configuration has the most states available to the electrons?

#### Henryk

Gold Member
This is an ill-posed question. If you look at hydrogen atoms, the allowed bound states have energies equal to $E_n = \frac {Ry} {n^2}$ and n is the main quantum number ranging from 1 to ... infinity. In other words, there is an infinite number of available electronic states in a single hydrogen atom. It is true for any atom as well. Now, when atoms form a solid, each of these atomic state is split into a band and within each band, there are as many allowed states as there are atoms in the entire solid (ok, strictly speaking, each band has as many states as there are primitive unit cells within the entire solid but number of bands gets multiplied by number of atoms within a primitive unit cell).
So, you have an infinite number of states multiplied by a very large number of atoms in a piece of solid.
Which infinity is greater?

#### ZapperZ

Staff Emeritus
2018 Award
To rephrase it. An electron in isolation has discrete value.
This is false. If you mean an electron "in isolation" as in free electron (i.e. not encumbered by any external potential), then it does not have "discrete values" in terms of the allowed energies and momentum. Try it. Solve the Schrodinger equation for a free electron.

When it is part of solid, The formerly discrete nature of allowed energies for an electron is turned into thick energy bands, within which electrons can occupy any energy they desire (well, almost). In this sense, you have many states available to the electrons.

Which of these... iron, quartz or semiconductors have most states available to the electrons?

What other solid configuration has the most states available to the electrons?
As has been stated, this is an ill-posed question. If you are talking about the density of states, then that's a different issues, because you will have to indicate the relevant bands and relevant energy and momentum range. Asking for a total number of states does not make sense.

And not only that, even for a particular solid, such as iron, changing its crystal structure can change its density of states. So just specifying an element alone, or a semiconductor alone, isn't sufficient.

Zz.

"Electron bands in solids"

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