Atomic Radius Problem with 286 pm Lattice Parameter

[vijayssonule]

i have one problem on atomic radius. i read (http://en.wikipedia.org/wiki/Atomic_radius) the artical and try to understand it but i don't found any formula for it.
The problem is:
if the lattice parameter of alpha iron is 286 pm (Pico meter),what is its atomic radius?
here we have only one variable Lattice parameter = 286 is given.
please help me to solve the problem.

 

[Astronuc]

See this discussion of atom sizes.
http://www.webelements.com/iron/atom_sizes.html

The atomic radius is approximately half the lattice parameter (l), or exactly for a simple cube, which has one atom at each corner of a cube, and so each atom is 'touching' is neighbor along the side/face of the cube.

Alpha-iron has a bcc structure, with one atom in the center of the cube, which touches the eight atoms on each corner of the cube, so that the atoms on the corners of the cube are separated and the lattice parameter is slightly greater than 2R, or R is slightly less the l/2.

Pick the a corner of the cube, and let the center atom be located at (l/2, l/2, l/2) of the cube of side, l. Find the distance from the center of the corner atom to center of the central atom, in terms of l, and that distance = 2R.

 

[oswaler]

Hello,

Thank you for reaching out with your question about atomic radius and lattice parameters. The atomic radius is a measure of the size of an atom, and it is typically defined as the distance from the center of the nucleus to the outermost electron orbital.

In order to solve this problem, we first need to understand the relationship between lattice parameter and atomic radius. The lattice parameter is the distance between the centers of neighboring atoms in a crystal structure. In other words, it is the distance between the nuclei of two neighboring atoms.

The atomic radius can be calculated by dividing the lattice parameter by two. This is because the atomic radius is half the distance between two neighboring atoms. So, in this case, the atomic radius of alpha iron would be 143 pm (286 pm / 2 = 143 pm).

I hope this helps you to understand the relationship between lattice parameter and atomic radius. If you have any further questions, please don't hesitate to ask. Keep up the good work in your studies!

Best regards,