Iron $($Fe$)$ undergoes an allotropic transformation at $912C$ : upon heating from a $BCC($a phase$)$ to an FCC $($Y phase$).$ Accompanying this transformation is a change in the atomic radius of $Fe-$from $R_{BCC}=0\mathrm{.}12584nm$ to $R_{FCC}=0\mathrm{.}12894nm-$and, in addition a change in density $($and volume$).$ Calculate the change in density related to this transformation.

a$.$ Write the relevant equation

b$.$ Calculate the volume of the a Fe phase

c$.$ How many atoms are in the unit cell of the a Fe phase?

d$.$ Calculate the density of the a Fe phase.

e$.$ Calculate the volume of the $Fe$ phase

f$.$ How many atoms are in the unit cell of the $F$ Fe phase?

g$.$ Calculate the density of the yFe phase.

h$.$ Does the density increase or decrease?