A single electron orbits around a stationary nucleus of charge $$+Ze$$ in a hydrogen-like atom, where $$Z$$ is the atomic number and $$e$$ is the magnitude of the charge on an electron. It requires $$47.25\,\text{eV}$$ to excite the electron from second Bohr orbit to the third Bohr orbit. Ionization energy of hydrogen atom is $$13.6\,\text{eV}$$. Then

A

the value of $$Z$$ is $$5$$

B

the energy required to excite the electron from the third orbit to the fourth orbit is $$16.53\,\text{eV}$$ nearly

C

the wavelength of electromagnetic radiation required to liberate the electron completely when in the first Bohr orbit is $$36.56\,\text{\AA}$$

D

the angular momentum of an electron in the second Bohr orbit is $$1.056\times10^{-33}\,\text{J s}$$