Question

An element with molar mass 27 g/mol forms cubic unit cell with edge length of 4.05x10-8 cm. If the density of the element is 2.7 g/cm3 Calculate the number of atoms present in the unit cell. Mention the factors on which the colour of a transition metal ion depends.​

Answer 1

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Answer 2

Given:

Molar mass of the given element, M=27gmol

−1

=0.027kgmol

−1

Edge length, a=4.05×10

−8

cm=4.05×10

−10

m

Density, d=2.7gcm

−3

=2.7×10

−3

kgm

3

We know that

d=

a

3

×N

A

Z×M

Where, Z is the number of atoms in the unit cell and N

A

is the Avogadro number.

Thus,

Z=

M

d×a

3

×N

A

Z=

0.027

2.7×10

3

(4.05×10

−10

)

3

×6.022×

23

(N

A

=6.022×10

23

)

Z=4orz≈4(fcc)

Since, the number of atoms in the unit cell is 4, the given cubic unit cell has face-centred cubic (fcc) or cubic-close packed (ccp) structure.

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