Final answer:
The d-spacing for a plane with Miller indices (1,1,0) in a cubic crystal with a lattice constant of 0.4 nm is calculated using the formula for interplanar spacing in cubic crystals, resulting in approximately 0.2828 nm.
Step-by-step explanation:
To calculate the d-spacing of a plane with Miller indices (1,1,0) in a cubic crystal where a = 0.4 nm, we can use the formula for the interplanar spacing in cubic crystals:
d_{hkl} = frac{a}{sqrt h^2 + k^2 + l^2
where d_{hkl} is the interplanar spacing, a is the lattice constant, and h, k, l are the Miller indices of the crystal plane.
For the (1,1,0) plane, the calculation would be:
d_{110} = frac{0.4 nm}{sqrt{1^2 + 1^2 + 0^2}} = frac{0.4 nm}{sqrt{2}} approx 0.2828 nm
Hence, the d-spacing for the (1,1,0) plane is approximately 0.2828 nm.