The wavelength of a spectral line emitted by a hydrogen atom in the Lyman series is $\frac{16}{15 R} \ cm$. What is the value of $n_2$? $(R = \text{Rydberg constant})$

The existence of a positively charged nucleus was established by:

Maximum number of spectral lines possible when an electron jumps from $5^{th}$ excited state to ground state in a sample containing only one Hydrogen atom will be

Based on the equation $E = -2.178 \times 10^{-18} \ J \left( \frac{Z^2}{n^2} \right)$,certain conclusions are written. Which of them is not correct?

In the ground state of $He^{+}$ ion,how much energy must be supplied to the electron so that the second line of the Balmer series is obtained in its spectrum? ................. $eV$

$(i)$ The energy associated with the first orbit in the hydrogen atom is $-2.18 \times 10^{-18} \, J \, atom^{-1}$. What is the energy associated with the fifth orbit?
$(ii)$ Calculate the radius of Bohr's fifth orbit for the hydrogen atom.