Sodium metal (atomic weight 22.99 g/cm^3) adopts a body-centered cubic structure with a density of 0.97 g/cm^3. (a) Use this information and Avogrado's number (Na=6.022x10^23) to estimate the atomic radius of sodium. (b) If it didn't react so vigorously, sodium could float on water. Use the answer from part (a) to estimate the density of Na if its structure were that of a cubic close-packed metal. Would it still float on the water?

The atomic radius of sodium is 185.59 pm.

Sodium metal will float in water.

Explanation:

a) To calculate the density of metal, we use the equation:

where,

= density  =

Z = number of atom in unit cell = 2  (BCC)

M = atomic mass of metal = 22.99 g/mol

= Avogadro's number =

a = edge length of unit cell = ?

Putting values in above equation, we get:

To calculate the radius, we use the relation between the radius and edge length for BCC lattice:

where,

R = radius of the lattice = ?

a = edge length = 428.6 pm

Putting values in above equation, we get:

The atomic radius of sodium is 185.59 pm.

b)

Density of water = D = 1 g/mL =

( )

Density of the sodium metal = d =

D > d ( float)

Since, the density of the sodium metal is less than the water's density which means that sodium metal will float in water.

periodic trends is an atom that gets larger as the number of electronic shells increase, the radius of atoms increases as you go down a certain group in the periodic table of elements. in general, the size of an atom will decrease as you move from left to right of a certain period.