Ionization potential of a hydrogen atom is $13.6 \text{ eV}$. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy $12.1 \text{ eV}$. According to Bohr's theory,the number of spectral lines emitted by the hydrogen atoms will be:

As the electron in a Bohr orbit of a Hydrogen atom transitions from state $n = 2$ to $n = 1$,how do the kinetic energy $K$ and potential energy $U$ change?

If the energy of the $n^{th}$ orbit in a hydrogen atom is $E_n$,what will be the energy of the $n^{th}$ orbit in a helium ion $(He^+)$?

Which of the following is quantized according to Bohr's theory of the hydrogen atom?

$A$ free hydrogen atom after absorbing a photon of wavelength $\lambda_{a}$ gets excited from the state $n=1$ to the state $n=4$. Immediately after that,the electron jumps to $n=m$ state by emitting a photon of wavelength $\lambda_{e}$. Let the change in momentum of the atom due to the absorption and the emission be $\Delta p_{a}$ and $\Delta p_{e}$,respectively. If $\lambda_{a} / \lambda_{e} = 1/5$,which of the following options is/are correct?
[Use $hc = 1242 \text{ eV nm}$; $1 \text{ nm} = 10^{-9} \text{ m}$,$h$ and $c$ are Planck's constant and speed of light,respectively]
$(1)$ $\lambda_{e} = 418 \text{ nm}$
$(2)$ The ratio of kinetic energy of the electron in the state $n=m$ to the state $n=1$ is $1/4$
$(3)$ $m=2$
$(4)$ $\Delta p_{a} / \Delta p_{e} = 1/2$

The energy required to remove one electron from a neutral helium atom is $24.6 \, eV$. The energy required to remove the remaining second electron (in $eV$) is .........