Chromium crystallises with a bcc lattice with unit cell edge length equal to 287 pm. The atomic radius of chromium atom is ______________.
Answers
Answer:
Explanation:
a=287 pm=2.87
A
˚
,
Z=2(BCC), M
A
=52
In body-centred cubic unit cell,
a
3
=4r
where, a= edge length, r= radius of atom
r=
4
a
3
=
4
3
×2.87
=1.2427
A
∘
Now,
ρ=
N
A
×a
3
Z×M
A
ρ=
6.023×10
23
×23.64×10
−24
2×52
=7.3 g/cm
3
Answer:
For body centred cubic cell atomic radius
r=
4
3
×edgelength
=
4
3
×287
=124.47pm
Thus, atomic radius of chromium metal is 124.27 pm.
Density of the unit cell of the solid =
Volumeofunitcell
Massofunitcell
Mass of unit cell = No. of atoms in unit cell (z)× mass of each atom (m)
For body centered cubic lattice, the number of atoms in unit cell (z) is
1+(
8
1
×8)=1+1=2
Mass of each atom (m)=
Avogadro
′
sno.
Atomicmass
=
6.023×10
23
52.99
The volume of the cubic lattice=(Edgelength)
3
=(287×10
−10
)
3
∴ Density of the unit cell is =
6.023×10
23
×(287)
3
×10
−30
2×52.99
gm/cm
3
7.44gm/cm
3
Thus, the density of chromium is gm/cm
3
is 7.44.