The series limit for the Balmer series of $H$ atom spectra is:

In a hydrogen atom,the energy difference between the states $n = 2$ and $n = 3$ is $E \ eV$. The ionization energy of the $H$-atom is: (in $E$)

State whether the following statements are true or false:
$(i)$ In Rutherford's atomic model,the Coulombic forces between the nucleus and electrons are mathematically similar to the gravitational forces $F = G \frac{m_1 m_2}{r^2}$.
$(ii)$ Out of every $20000$ $\alpha$-particles,$\sim 10$ particles bounce back after hitting the gold foil.
$(iii)$ In Rutherford's experiment,a zinc sulfide $(ZnS)$ fluorescent screen is placed around the gold foil.
$(iv)$ Rutherford's $\alpha$-particle scattering experiment is related to the size of the atomic nucleus.

Calculate the energy in joule corresponding to light of wavelength $45 \ nm$. (Planck's constant,$h = 6.63 \times 10^{-34} \ J \ s$,speed of light,$c = 3 \times 10^8 \ m \ s^{-1}$)

If the wavelength of the first line of the Paschen series of a hydrogen atom is $720 \ nm$,then the wavelength of the second line of this series is $.......... \ nm$. (Nearest integer)

An electronic transition in a hydrogen atom results in the formation of the $H_\alpha$ line of the hydrogen spectrum in the Lyman series. The energies associated with the electron in each of the orbits involved in the transition (in $kcal \ mol^{-1}$) are: