In Bohr's model of an atom,when an electron jumps from $n = 1$ to $n = 3$,how much energy is absorbed?

The ionization energy of a hydrogen atom is $13.6 \ eV$. The energy required to excite the electron in a hydrogen atom from the ground state $(n=1)$ to the first excited state $(n=2)$ is (Note: The question asks for energy per atom in Joules. Given $1 \ eV = 1.602 \times 10^{-19} \ J$)

The frequency of a certain line of the Lyman series of the atomic spectrum of the $H$ atom satisfies the following conditions:
$(i)$ It is the sum of the frequency of another Lyman line and a Balmer line.
$(ii)$ It is the sum of the frequency of a certain line,a Lyman line,and a Paschen line.
$(iii)$ It is the sum of the frequency of a Lyman and a Paschen line but no Brackett line.
To what transition does this frequency correspond?

In the transition of an electron in an atom,its kinetic energy changes from $y$ to $y/4$. The change in potential energy $(P.E.)$ will be:

In which transition of the hydrogen atom will the emitted radiation have the lowest frequency?

The radius of the second Bohr orbit is $x$. The de-Broglie wavelength of an electron in the $4^{th}$ orbit is nearly