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I was given this problem recently to compute the number of ions in a unit cell of ferrous oxide $\ce{FeO}$. The data given was:

Side length $a = \pu{5 Å}$

 

Density $d = \pu{4 g/cc}$

Using the formula $\displaystyle d = \frac {ZM}{N_0 a^3}$, I obtained $Z = 4.18$. However, the answer had rounded $Z$ off to $4.$

Could a unit cell have a fractional number of atoms? Intuitively, it doesn't make sense for a cell to have $0.18$ of an atom. If, by experimental analysis, we obtain a fractional number of atoms in a unit cell, do we round them down as is done in this problem?

P.S. Another thought would be that such odd numbers are obtained due to stoichiometric defects.

I was given this problem recently to compute the number of ions in a unit cell of ferrous oxide $\ce{FeO}$. The data given was:

Side length $a = \pu{5 Å}$

 

Density $d = \pu{4 g/cc}$

Using the formula $\displaystyle d = \frac {ZM}{N_0 a^3}$, I obtained $Z = 4.18$. However, the answer had rounded $Z$ off to $4.$

Could a unit cell have a fractional number of atoms? Intuitively, it doesn't make sense for a cell to have $0.18$ of an atom. If, by experimental analysis, we obtain a fractional number of atoms in a unit cell, do we round them down as is done in this problem?

P.S. Another thought would be that such odd numbers are obtained due to stoichiometric defects.

I was given this problem recently to compute the number of ions in a unit cell of ferrous oxide $\ce{FeO}$. The data given was:

Side length $a = \pu{5 Å}$

Density $d = \pu{4 g/cc}$

Using the formula $\displaystyle d = \frac {ZM}{N_0 a^3}$, I obtained $Z = 4.18$. However, the answer had rounded $Z$ off to $4.$

Could a unit cell have a fractional number of atoms? Intuitively, it doesn't make sense for a cell to have $0.18$ of an atom. If, by experimental analysis, we obtain a fractional number of atoms in a unit cell, do we round them down as is done in this problem?

P.S. Another thought would be that such odd numbers are obtained due to stoichiometric defects.

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andselisk ♦
andselisk ♦
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I was given this problem recently to compute the number of ions in a unit cell of Ferrousferrous oxide $\ce{FeO}$. The data given was:

Side length $a = \pu{5 Å}$

Density $d = \pu{4 g/cc}$

Using the formula $d = \frac {ZM}{N_0 a^3}$$\displaystyle d = \frac {ZM}{N_0 a^3}$, I obtained $Z = 4.18$. However, the answer had rounded Z$Z$ off to 4.$4.$

Could a unit cell have a fractional number of atoms? ItIntuitively, it doesn't make intuitional sense for a cell to have 0.18$0.18$ of an atom. If, by experimental analysis, we obtain a fractional number of atoms in a unit cell, do we round them down as is done in this problem?

P.s: anotherS. Another thought would be that such odd numbers are obtained due to stoichiometric defects.

I was given this problem recently to compute the number of ions in a unit cell of Ferrous oxide $\ce{FeO}$. The data given was:

Side length $a = \pu{5 Å}$

Density $d = \pu{4 g/cc}$

Using the formula $d = \frac {ZM}{N_0 a^3}$, I obtained $Z = 4.18$. However, the answer had rounded Z off to 4.

Could a unit cell have a fractional number of atoms? It doesn't make intuitional sense for a cell to have 0.18 of an atom. If, by experimental analysis, we obtain a fractional number of atoms in a unit cell, do we round them down as is done in this problem?

P.s: another thought would be that such odd numbers are obtained due to stoichiometric defects.

I was given this problem recently to compute the number of ions in a unit cell of ferrous oxide $\ce{FeO}$. The data given was:

Side length $a = \pu{5 Å}$

Density $d = \pu{4 g/cc}$

Using the formula $\displaystyle d = \frac {ZM}{N_0 a^3}$, I obtained $Z = 4.18$. However, the answer had rounded $Z$ off to $4.$

Could a unit cell have a fractional number of atoms? Intuitively, it doesn't make sense for a cell to have $0.18$ of an atom. If, by experimental analysis, we obtain a fractional number of atoms in a unit cell, do we round them down as is done in this problem?

P.S. Another thought would be that such odd numbers are obtained due to stoichiometric defects.

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Aniruddha Deb
Aniruddha Deb
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Does a unit cell have to contain a whole number of atoms?

I was given this problem recently to compute the number of ions in a unit cell of Ferrous oxide $\ce{FeO}$. The data given was:

Side length $a = \pu{5 Å}$

Density $d = \pu{4 g/cc}$

Using the formula $d = \frac {ZM}{N_0 a^3}$, I obtained $Z = 4.18$. However, the answer had rounded Z off to 4.

Could a unit cell have a fractional number of atoms? It doesn't make intuitional sense for a cell to have 0.18 of an atom. If, by experimental analysis, we obtain a fractional number of atoms in a unit cell, do we round them down as is done in this problem?

P.s: another thought would be that such odd numbers are obtained due to stoichiometric defects.