A hydrogen atom is in its ground state

$($ni $=1)$

when a photon impinges upon it$.$

The atom absorbs the photon, which has precisely the energy required to raise the atom to the

nf $=3$

state.

$($a$)$

$($a$)$

What is the initial quantum number,

ni$,$

of the transition that generates the photon with the longest wavelength? $($Restrict your attention to the four illustrated transitions.$)$

ni $=$