47. A certain form of lead has a cubic closest packed structure with an edge length of 492 pm. Calculate the value of the atomic radius and the density of lead. 48. You are given a small bar of an unknown metal X. You find the density of the metal to be 10.5g/cm^3 . An X-ray diffraction ex- periment measures the edge of the face-centered . cubic unit cell as 4.09hat (A)(1hat (A)=10^-10m) . Identify X.

47. To calculate the atomic radius of lead in a cubic closest packed structure with an edge length of 492 pm, we can use the relationship between the edge length and the atomic radius in a closest packed structure. The edge length is equal to twice the atomic radius. Therefore, the atomic radius of lead is half of the edge length, which is 492 pm / 2 = 246 pm.<br /><br />To calculate the density of lead, we can use the formula for density, which is mass divided by volume. The mass of a cubic unit cell can be calculated using the formula for the volume of a cube, which is edge length cubed. Therefore, the mass of a cubic unit cell is (492 pm)^3 * density of lead. The volume of a cubic unit cell is (492 pm)^3. Therefore, the density of lead is mass/volume = (492 pm)^3 * density of lead / (492 pm)^3 = density of lead.<br /><br />48. To identify the unknown metal X, we can use the given density and the edge length of the face-centered cubic unit cell to calculate the atomic mass of the metal. The density of a metal is equal to the mass of the metal divided by the volume of the unit cell. The volume of a face-centered cubic unit cell can be calculated using the formula for the volume of a cube, which is edge length cubed. Therefore, the volume of the unit cell is (4.09 x 10^-10 m)^3. The mass of the metal can be calculated by multiplying the density by the volume of the unit cell. The atomic mass of the metal can be calculated by dividing the mass of the metal by Avogadro's number (6.022 x 10^23 atoms/mol). By comparing the calculated atomic mass with the known atomic masses of elements, we can identify the unknown metal X.