If the potential energy of a hydrogen atom in the first excited state is assumed to be zero, then the total energy of n = $$\infty$$ state is,

If the kinetic energies of an electron, an alpha particle and a proton having same de-Broglie wavelength are $${\varepsilon _1},{\varepsilon _2}$$ and $${\varepsilon _3}$$ respectively, then

Suppose in a hypothetical world the angular momentum is quantized to be even integral multiples of $${h \over {2\pi }}$$. The largest possible wavelength emitted by hydrogen atoms in visible range in a world according to Bohr's model will be,

(Consider hc = 1242 Mev-fm)