The unit cell of a metallic element is face centred cubic and the side of the cube is 540.2 pm. Calculate the density of a metal in gcm-3 is if its relative atomic mass is 202.4.
Answers
Answered by
29
Given:
Edge of cube, a = 540.2 pm = 540.2 × 10⁻¹⁰ cm
Atomic mass, M = 202.4 gm
The unit cell is FCC.
To Find:
The density of the metal.
Calculation:
- For FCC, z = 4
- We know the formula:
V × NA × d = z × M
⇒ a³ × NA × d = z × M
⇒ d = (z × M)/(a³ × NA)
⇒ d = (4 × 202.4)/{(540.2 × 10⁻¹⁰)³ × 6.022 × 10²³)
⇒ d = 809.6/(157.64 × 10⁻²⁴ × 6.022 × 10²³)
⇒ d = 809.6/94.93
⇒ d = 8.528 gm/cm³
- So, the density of the given metallic element is 8.528 gm/cm³.
Answered by
3
We know that,
Density-
d=
a
3
×NA
Z×M
Given :
Molar Mass(M)=108g/mol
Density (d)=10.5g/cm
3
Edge Length(a)=409pm
Z=
M
d×a
3
×N
A
Value of N
A
is N
A
=6.023×10
23
Z=
108
10.5×(409×10
−10
cm
3
)
3
×6.023×10
23
=4
Number of atoms =4
Hence the element is packed in FCC structure.
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