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The "OLIVINE" series of minerals consist...

The `"OLIVINE"` series of minerals consists of crystal in which `Fe^(2+)` and `Mg^(2+)` ions may substitute for each other causing susbstitutional impurity defects without changing the volume of unit cell. In `"OLIVINE"` series of minerals, `O^(2-)` ions exist as fcc with `Si^(4+)` occupying one-fourth of `OVs` and divalent metal ions occupying one-fourth of `OVs` and divalent metal ions occupying one-fourth of `TVs`. The density of "forsterite" (magnesium silicate) is `3.21 g cm^(-3)` land that of "fayalite" (ferrous silicate) is `4.34 g cm^(-3)`.
The formula of "fayalite mineral" is

A

`Fe_(2)SiO_(4)`

B

`FeSiO_(4)`

C

`Fe_(2)SiO_(6)`

D

`Fe_SiO_(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
For fcc,
Number of `O^(2-)` ion=`8 ("corner") xx (1)/(8) "per corner share"` ltbr. `+ 6 ("faces") xx (1)/(2) "per face share"`
`= 4`
Number of `Si^(4+)` ions `= 1/4 xx "OV" = 1/4 xx 4 = 1//"unit cell"`
Number of `Fe^(2+)` ions `= 1/4 xx "TV" = 1/4 xx 8 = 2//"unit cell"`
So, formula of `"FAYLITE"` is `overset(+2xx2)(Fe_(2))Si^(4+)O_(4^(2-))`
`rArr Fe_(2)SiO_(4)`
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The "OLIVINE" series of minerals consists of crystal in which Fe^(2+) and Mg^(2+) ions may substitute for each other causing susbstitutional impurity defects without changing the volume of unit cell. In "OLIVINE" series of minerals, O^(2-) ions exist as fcc with Si^(4+) occupying one-fourth of OVs and divalent metal ions occupying one-fourth of OVs and divalent metal ions occupying one-fourth of TVs . The density of "forsterite" (magnesium silicate) is 3.21 g cm^(-3) land that of "fayalite" (ferrous silicate) is 4.34 g cm^(-3) . If in "forsterite mineral" bivalent Mg^(2+) ions are to be replaced by unipositive Na^(o+) ions, and if Na^(o+) ions are occupying half of TV_(s) in fcc lattice, the arrangement of rest of the constituents is kept same, then the formula of the new solid is:

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