Final answer:
The radius of gyration for polyethylene is approximately 4.74 nm.
Step-by-step explanation:
The radius of gyration for a polymer can be calculated using the formula:
Rg = sqrt(N*L^2/6)
Where:
N = number of monomers
L = bond length of the monomer
In this case, polyethylene has 1,000 monomers and a bond length of 0.15 nm.
Plugging these values into the formula, we get:
Rg = sqrt(1000*0.15^2/6)
= sqrt(22.5)
= 4.74 nm
Therefore, the radius of gyration for polyethylene is approximately 4.74 nm.