(Solved): d. Below is a face-centered unit cell, write the letter "a" along the edge length. Look at the dia ...

d. Below is a face-centered unit cell, write the letter "a" along the edge length. Look at the diagonal along the face. Calculate the length of the diagonal if all sides are "a". (Hint: Use the Pythagorean relationship \( c^{2}=a^{2}+b^{2} \) ) Answer: e. Notice that the face atom and the corner atoms along the diagonal all touch. Solve for the length of the diagonal in terms of " \( r \) " the radius of one atom. Answer: f. Solve for " \( \mathrm{a} \) " in terms of " \( \mathrm{r} \) " for a face-centered cubic cell. (Hint: Since question \( 3 d \) and 3e express the length of the diagonal when the side is " \( a \) " set them equal and solve for " \( a \) ", the side of length of a face-centered unit cube.) Answer: