Final answer:
The atomic radius of an unknown metal with a BCC structure with a unit cell edge length of 4.35 Å can be calculated using the geometry of a cube, yielding an atomic radius of approximately 1.88 Å. The correct answer is E.
Step-by-step explanation:
The question concerns determining the atomic radius of an unknown metal which crystallizes in a body-centered cubic (BCC) structure with a given unit cell edge length. In a BCC structure, the length of the diagonal passing through the center of the unit cell which connects two opposite corners is equivalent to four atomic radii (4r) and also can be related to the edge length (a) through the geometry of the cube (the diagonal is √3 times the edge length).
The relation is given by 4r = √3a.
To calculate the atomic radius, we plug in the edge length of 4.35 Å (angstroms):
4r = √3 * 4.35 Å
r = (√3 * 4.35 Å) / 4
r ≈ 1.88 Å
Therefore, the correct answer is E, 1.88 Å.