An element crystalizes in a FCC?

[匿名]

2017-02-21 1:00 pm

An element crystalizes in a FCC unit cell and has a density of 19.3g/cm3. The atomic radius is 321 pm. Calculate an approximate molar mass for this element.

回答 (1)

wanszeto

2017-02-21 3:24 pm

✔ 最佳答案

The diagonal of the face a unit cell of FCC
= 4 × (atomic radius)
= 4 × (321 pm)
= 1284 pm

The length of edge of a unit cell
= 1284/√2 pm
= (1284/√2) × 10⁻¹⁰ cm

The volume of a unit cell
= [(1284/√2) × 10⁻¹⁰]³ cm³

Mass of a unit cell
= {[(1284/√2) × 10⁻¹⁰]³ cm³} × (19.3 g/cm³)
= (1284/√2)³ × 10⁻³⁰ × 19.3 g

Number of atoms in a unit cell
= 8 × (1/8 atom at corner) + 6 × (1/2 atom on face)
= 4 atoms

No. of moles of atoms in a unit cell
= [4/(6.022 × 10²³)] mol

Molar mass for the element
= [(1284/√2)³ × 10⁻³⁰ × 19.3 g] / {[4/(6.022 × 10²³)] mol}
= 2174 g/mol

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