The correct representation of the wavelength-intensity relationship of an ideal black body radiation at two different temperatures $T_{1}$ and $T_{2}$ (where $T_{2} > T_{1}$) is:

The radius of the second Bohr orbit for hydrogen atom is .......... $\mathring{A}$.
(Planck's constant $h = 6.626 \times 10^{-34} \, Js$; mass of electron $= 9.1091 \times 10^{-31} \, kg$; charge of electron $e = 1.60210 \times 10^{-19} \, C$; permittivity of vacuum $\epsilon_0 = 8.854185 \times 10^{-12} \, C^2 N^{-1} m^{-2}$)

For a hydrogen $(H)$ atom,what will be the wavelength (in $nm$) associated with the transition of an electron from the infinite energy level to the first energy level? (Rydberg constant = $1.097 \times 10^{7} \ m^{-1}$)

When an electron transitions from the $n^{th}$ orbit to the $2^{nd}$ orbit in a $Li^{2+}$ ion,$15$ spectral lines are obtained. What is the value of $n$?

What is the angular momentum of an electron in the orbit of an $H$ atom where the energy of the electron is $-3.4 \ eV$?

What transition in $He^{+}$ ion shall have the same wave number as the first line in Balmer series of hydrogen atom?