Titanium has an hcp unit cell for which the ratio of the lattice parameters cais 1.58. if the radius of the be atom is 0.1445 nm, (a) determine the unit cell volume, and (b) calculate the theoretical density of ti, given that its atomic weight is 47.87 g/mol

Answer :

(a) The volume of unit cell is,

(b) The theoretical density of Ti is,

Explanation :

(a) First we have to calculate the volume of the unit cell.

Formula used :

where,

V = volume of unit cell  = ?

r = atomic radius =

conversion used :

Ratio of lattice parameter = c : a = 1.58 : 1

So, c = 1.58 a

And,  a = 2r

c = 1.58 × 2r

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

The volume of unit cell is,

(b) Now we have to calculate the density of Ti.

Formula used for density :

    ..........(1)

where,

= density  of Ti = ?

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

M = atomic mass  = 47.87 g/mol

= Avogadro's number  =

= volume of unit cell  =

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

The theoretical density of Ti is,

can you attach a picture of the lettuce? : )

the correct option is c.

isotopes refers to different forms of the same element with the same atomic number but different mass number as a result of difference in their neutron numbers. isotopes have different relative atomic mass but share the same chemical properties.