The density of zinc is 7.14 g/cm^3 and has an atomic radius of 1.332a. calculate the height of its unit cell. the atomic weight is 65.37 grams/mole.

Answer : The height of the unit cell is,

Explanation : Given,

Density of zinc =

Atomic radius =

Atomic weight of zinc = 65.37 g/mole

As we know that, zinc has haxagonal close packed crystal structure. The number of atoms in unit cell of HCP is, 6.

Formula used for density :

     .............(1)

where,

= density  of zinc

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

M = atomic mass

= Avogadro's number  =

a = edge length of unit cell

= volume of unit cell

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

Now we have to calculate the height of the unit cell.

Formula used :

where,

V = volume of unit cell

r = atomic radius =

conversion used :

h = height of the unit cell

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

Therefore, the height of the unit cell is,

you'd use the equation that establishes a relationship between  energy  and  wavelength, which looks like this

e=h⋅cλ, where

λ  - the wavelength of the photon; c  - the speed of light, usually given as  3⋅108m/s; h  -  planck's constant, equal to  6.626⋅10−34j s

plug the value you were given for the energy of the photon in the above equation to get the wavelength

e=h⋅cλ⇒λ=h⋅ce

λ=6.626⋅10−34js⋅3⋅108ms−1.257⋅10−24j=1.581⋅10−1m