Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be

Figure shows two semicircular loops of radii $$R_1$$ and $$R_2$$ carrying current $I$. The magnetic field at the common centre '$$\mathrm{O}$$' is

When radiation of wavelength '$$\lambda$$' is incident on a metallic surface, the stopping potential is 4.8 V. If the surface is illuminated with radiation of double the wavelength then the stopping potential becomes $$1.6 \mathrm{~V}$$. The threshold wavelength for the surface is

A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having $$\mathrm{n}$$ turns. If the same current passes in both the cases, the ratio of magnetic fields produced at the centre for one turn to that of $$n$$ turns is