In the hydrogen spectrum,if an electron transitions from the $6^{th}$ orbit to the $3^{rd}$ orbit,what is the total number of spectral lines observed in the infrared region?

If '$X$' is the ionization energy of hydrogen,then the energy required for the excitation of a $Li^{2+}$ electron from the $2^{nd}$ excited state to the $5^{th}$ excited state is:

Bohr's model cannot explain the emission spectrum of

For $Li^{2+}$,the ratio of radii $r_2 : r_5$ is:

$A$ bulb of $40 \ W$ is producing light of wavelength $620 \ nm$ with $80 \%$ efficiency. The number of photons emitted by the bulb in $20 \ s$ is $(1 \ eV = 1.6 \times 10^{-19} \ J, hc = 12400 \ eV \ \mathring{A})$

Match the spectral series of the hydrogen atom given in List-$I$ with their corresponding transitions given in List-$II$.

List-$I$	List-$II$
$(1)$ Lyman	$(A)$ $n = 2 \to n = 1$
$(2)$ Balmer	$(B)$ $n = 3 \to n = 2$
$(3)$ Paschen	$(C)$ $n = 4 \to n = 3$
$(4)$ Brackett	$(D)$ $n = 5 \to n = 4$