An $$\alpha $$-particle of energy $$5$$ $$MeV$$ is scattered through $${180^ \circ }$$ by a fixed uranium nucleus. The distance of closest approach is of the order of

A piece of copper and another of germanium are cooled from room temperature to $$77K,$$ the resistance of

The manifestation of band structure in solids is due to

The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index $$n$$) is :