You are measuring the lattice constant (the distance between planes of atoms) of a sample crystal using X-ray diffraction. The crystal structure is known to be SC or simple cubic. Your X-ray tube produces X-rays with a wavelength of 0.260 nm. You observe the first diffraction peak at an angle of 18.9°. What is the lattice constant of the crystal?

Uranium has two naturally occurring isotopes. 238u has a natural abundance of 99.3% and 235u has an abundance of 0.7%. it is the rarer 235u that is needed for nuclear reactors. the isotopes are separated by forming uranium hexafluoride uf6, which is a gas, then allowing it to diffuse through a series of porous membranes. 235uf6 has a slightly larger rms speed than 238uf6 and diffuses slightly faster. many repetitions of this procedure gradually separate the two isotopes. what is the ratio of the rms speed of 235uf6 to that of 238uf6? express your answer to five significant figures.