On crystallisation of a solid metal (atomic mass 52) a body centred cubic lattice is formed. If its unit cell

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Q. On crystallisation of a solid metal (atomic mass 52) a body centred cubic lattice is formed. If its unit cell edge length is 287 pm, calculate the radius of the atom and density of the solid metal. (1+1+1) OR What are Osmosis and Osmotic pressure? What is Hypertonic solution? (1+1+1)

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For a BCC lattice, $4r=\sqrt3\,a$ gives the atomic radius, and $\rho=\dfrac{Z\cdot M}{N_A\cdot a^3}$ (with Z = 2 for BCC) gives the density.

Step 1 — Radius from the BCC geometry:

In a body-centred cubic lattice, atoms touch along the body diagonal, so $4r=\sqrt3\,a$ , i.e. $r=\dfrac{\sqrt3\,a}{4}$ .

Given $a = 287\text{ pm}$ :

$r=\dfrac{1.732\times287}{4}=\dfrac{497.1}{4}\approx124.2\text{ pm}$

Step 2 — Density:

For BCC, number of atoms per unit cell $Z=2$ (1 corner-share + 1 body-centre).

$a = 287\text{ pm} = 2.87\times10^{-8}\text{ cm}$ , so $a^3 = 2.364\times10^{-23}\text{ cm}^3$ . …

Q.On crystallisation of a solid metal (atomic mass 52) a body centred cubic lattice is formed. If its unit cell edge length is 287 pm, calculate the radius of the atom and density of the solid metal. (1+1+1) OR What are Osmosis and Osmotic pressure? What is Hypertonic solution? (1+1+1)