Titanium has an HCP crystal structure, a c/a ratio of 1.669, an atomic weight of 47.87 g/mol, and a density of 4.51 g/cm3. Compute the atomic radius for Ti.

Answer : The atomic radius for Ti is,

Explanation :

Atomic weight = 47.87 g/mole

Avogadro's number

First we have to calculate the volume of HCP crystal structure.

Formula used :  

.............(1)

where,

= density  =

Z = number of atom in unit cell (for HCP = 6)

M = atomic mass  = 47.87 g/mole

= Avogadro's number  

V = volume of HCP crystal structure = ?

Now put all the values in above formula (1), we get

Now we have to calculate the atomic radius for Ti.

Formula used :

Given:

c/a ratio = 1.669 that means,  c = 1.669 a

Now put (c = 1.669 a) and (a = 2R) in this formula, we get:

Now put all the given values in this formula, we get:

Therefore, the atomic radius for Ti is,

metric time was an attempt to create a standard unit of time based off of 10, but it never took off an is not included in the metric system (si)