An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is (are) true?

A hydrogen atom in its ground state is irradiated by light of wavelength 970$$\mathop A\limits^o $$.

Taking hc = 1.237 $$\times$$ 10^$$-$$6 eVm and the ground state energy of hydrogen atom as $$-$$ 13.6 eV, the number of lines present in the emission spectrum is

The isotope $$_5^{12}B$$ having a mass 12.014 u undergoes $$\beta $$-decay to $$_6^{12}C$$. $$_6^{12}C$$ has an excited state of the nucleus ($$_6^{12}C$$*) at 4.041 MeV above its ground state. If $$_5^{12}B$$ decays to $$_6^{12}C$$*, the maximum kinetic energy of the $$\beta$$-particle in units of MeV is (1u = 931.5 MeV/c², where c is the speed of light in vacuum).

An infinite line charge of uniform electric charge density l lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material of permittivity e and electrical conductivity s. The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density j (t) at any point in the material?