Q. 144.2( 27 Votes )

# If the radius of the octahedral void is r and radius of the atoms in close packing is R, derive relation between r and R.

Answer :

In the given figure, let the sphere have the centre, O and is fitted in the octahedral void.

As given, radius of the sphere fitted in the octahedral void = r

And the radius of the atoms in close packing = R

Here, angle AOD = 90^{0}

In triangle AOD,

DA^{2} = OA^{2} + OD^{2}

⇒ (R+R)^{2} = ( R + r )^{2}+ (R+r)^{2}

⇒ 4R^{2} = 2(R+r)^{2}

⇒ 2R^{2} = (R+r)^{2}

⇒ √2 R = (R+r)

⇒ R + r = R

⇒ r = R – R

⇒ r = R (1.414 - 1)

⇒ r = 0.414 R

This is the required relation between r and R.

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An element ‘*X*’ (At. mass = 40 g mol^{–1}) having f.c.c. structure, has unit cell edge length of 400 pm. Calculate the density of ‘*X*’ and the number of unit cells in 4 g of ‘*X*’. (*N _{A}* = 6.022 × 10

^{23}mol

^{–1})

Note : In the following questions a statement of assertion followed by a statement of reason is given. Choose the correct answer out of the following choices.

Chemistry - ExemplarThe correct order of the packing efficiency in different types of unit cells is ________.

Chemistry - ExemplarThe edge lengths of the unit cells in terms of the radius of spheres constituting fcc, bcc and simple cubic unit cell are respectively________.

Chemistry - ExemplarWhich of the following lattices has the highest packing efficiency

(i) simple cubic

(ii) body-centred cubic and

(iii) Hexagonal close-packed lattice?

NCERT - Chemistry Part-I