(a) compute the radius r of an impurity atom that will just fit into an fcc octahedral site in terms of the atomic radius r of the host atom (without introducing lattice strains). entry field with correct answer 0.414 r

radius r is  0.414 R

Explanation:

Given data

FCC octahedral site

atomic radius R

to find out

radius r

solution

we know that at FCC octahedral

length of side = 2 R + 2r

and by pythagorean theorem

a = 2√2R

here a = 2R + 2r

so 2R + 2r = 2√2R

so r = ( √2R )- R

r = 0.414 R

so  radius r is  0.414 R

root word, prefixes, and suffixes

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft