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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)`.
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:

A

`Na_(2)SiO_(4)`

B

`Na_(2)SiO_(3)`

C

`Na_(4)SiO_(4)`

D

`Na_(2)Si_(2)O_(6)`

Text Solution

Verified by Experts

The correct Answer is:
C
Number of `Na^(o+)` ions in fcc `= 1/2 xx TV = 1/2 xx 8`
`= 4//"unit cell"`
So, formula of solid `=overset(+1xx4)(Na_(4))Si^(4+)O_(4^(2-)) rArr Na_(4)SiO_(4)`
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