Which of the following energy changes is less than the third Balmer transition in the $He^{\oplus}$ ion?

State whether the following statements are true or false:
$(i)$ When an electron in a hydrogen atom returns from the third excited state to the ground state,it emits frequencies corresponding to lines in the Lyman,Balmer,and Paschen series.
$(ii)$ When an electron in a hydrogen atom returns from the third excited state to the ground state,it emits radiation with wavelengths corresponding to the Pfund series,which has very high frequencies.

Which of the following is the energy of a possible excited state of hydrogen? $........... \ eV$

The statements
$i$. In filling a group of orbitals of equal energy,it is energetically preferable to assign electrons to empty orbitals rather than pair them into a particular orbital.
$ii$. When two electrons are placed in two different orbitals,energy is lower if the spins are parallel.
Are valid for

When the frequency of light incident on a metallic plate is doubled,the $KE$ of the emitted photoelectrons will be:

Find the ionization energy and the wavelength of the photon emitted for a hydrogen atom transition from $n_1 = 2$ to $n_2 = \infty$.