The unit cell with all sides the same length and all angles equal to 90 degrees that has lattice points only at the corners is called

monoclinic
body-centered cubic
primative cubic
face-centered cubic
spherical cubic

try primitive cubic

primitive ccubic

The unit cell with all sides the same length and all angles equal to 90 degrees that has lattice points only at the corners is called a primitive cubic unit cell.

The unit cell described, with all sides the same length and all angles equal to 90 degrees and lattice points only at the corners, is known as the "primitive cubic" unit cell.

To arrive at this answer, we can break down and analyze the given options.

1. Monoclinic: A monoclinic unit cell does not satisfy the criteria mentioned, as its angles are not all equal to 90 degrees.

2. Body-centered cubic (BCC): A BCC unit cell has lattice points at both the corners and the center of the cube. The presence of the central lattice point violates the given condition.

3. Primitive cubic: A primitive cubic unit cell has lattice points solely at the corners, as described in the question. It is also characterized by having all sides of equal length and angles of 90 degrees.

4. Face-centered cubic (FCC): An FCC unit cell has additional lattice points on each face, in addition to those at the corners. Therefore, it does not match the criteria outlined.

5. Spherical cubic: There is no such thing as a "spherical cubic" unit cell, and it is not related to the given condition.

Thus, the correct answer is the "primitive cubic" unit cell.