In a hydrogen atom in its ground state, the first Bohr orbit has radius $r_1$. The electron's orbital speed becomes one-third when the atom is raised to one of its excited states. The radius of the orbit in that excited state is

The angular momentum of the electron in the third Bohr orbit of hydrogen atom is ' $l$ '. Its angular momentum in the fourth Bohr orbit is

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (a) second to first energy level and (b) highest energy level to second level is

If 'T' is the half life of a radioactive substance then its instantaneous rate of change of activity is proportional to