The radius of innermost orbit of hydrogen atom is $5.3 \times 10^{-11} \mathrm{~m}$. The radius of fourth allowed orbit of hydrogen atom is

In the third orbit of hydrogen atom the energy of an electron ' $E$ '. In the fifth orbit of helium $(Z=2)$ the energy of an electron will be

Ratio of longest wavelength corresponding to Lyman and Balmer series in hydrogen spectrum is

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