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Polonium metal crystallizes in a lattice which contains onlyone Po atom per cubi

ID: 690865 • Letter: P

Question

Polonium metal crystallizes in a lattice which contains onlyone Po atom per cubic unit cell. The radius of a polonium atom is1.67 Å. a) What type of cubic unit cell is observed in poloniummetal? b) What is the edge length of one polonium unit cell? c) Determine the density of polonium metal. - not just answer, a little explanation would be great!! Polonium metal crystallizes in a lattice which contains onlyone Po atom per cubic unit cell. The radius of a polonium atom is1.67 Å. a) What type of cubic unit cell is observed in poloniummetal? b) What is the edge length of one polonium unit cell? c) Determine the density of polonium metal. - not just answer, a little explanation would be great!!

Explanation / Answer

Since it has only one atom per unit cell it belongs to Simplecubic.
For Simple cubic structure , radius , r = Edge length( a) /2 So Edge length , a = 2r                            = 2 * 1.67 A o                           = 3.34 A o Volume of the unit cell , V = a^3                                        = (3.34*10^-8cm) ^3                                        = 37.2597 * 10^-24cm^3 Mass of one unit cell = ( Atomic mass * no. ofatoms per unit cell ) / Avagadro number                                = ( 209 * 1 ) / ( 6.023 * 10^23 )                                = 34.7 * 10^-23 g So density , d = mass of the one unit cell / Volume of unitcell                     = 34.7 * 10^-23 g / 37.2597* 10^-24 cm^3                      =9.3113 g / cm^3 Volume of the unit cell , V = a^3                                        = (3.34*10^-8cm) ^3                                        = 37.2597 * 10^-24cm^3 Mass of one unit cell = ( Atomic mass * no. ofatoms per unit cell ) / Avagadro number                                = ( 209 * 1 ) / ( 6.023 * 10^23 )                                = 34.7 * 10^-23 g So density , d = mass of the one unit cell / Volume of unitcell                     = 34.7 * 10^-23 g / 37.2597* 10^-24 cm^3                      =9.3113 g / cm^3