Which of the following electron transitions in a hydrogen atom will require the largest amount of energy?

In the hydrogen spectrum,the energy during the first Lyman transition is $E = 10.2 \ eV$. The same energy is observed during the second Balmer series transition in which of the following species?

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.

Identify the pair of species having the same energy from the following (The number given in the bracket corresponds to the principal quantum number $(n)$ in which the electron is present).

What is the wave number of the lowest energy transition associated with the Lyman series?

If the frequency of radiation emitted for the electron transition from an excited state to ground state of hydrogen atom is $\frac{3 X}{4} \ Hz$,the frequency of radiation absorbed for the electron transition from the above excited state to the next immediate excited state in $Hz$ is: