For $\mathrm{He}^{+}$, a transition takes place from the orbit of radius $105.8 \mathrm{pm}$ to the orbit of radius $26.45 \mathrm{pm}$. The wavelength (in nm) of the emitted photon during the transition is _______.

[Use :

Bohr radius, $\mathrm{a}=52.9 \mathrm{pm}$

Rydberg constant, $R_{\mathrm{H}}=2.2 \times 10^{-18} \mathrm{~J}$

Planck's constant, $\mathrm{h}=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}$

Speed of light, $\mathrm{c}=3 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$ ]

Consider a helium (He) atom that absorbs a photon of wavelength 330 nm. The change in the velocity (in cm s^$$-$$1) of He atom after the photon absorption is __________.

(Assume : Momentum is conserved when photon is absorbed.

Use : Planck constant = 6.6 $$\times$$ 10^$$-$$34 J s, Avogadro number = 6 $$\times$$ 10²³ mol^$$-$$1, Molar mass of He = 4 g mol^$$-$$1)

The figure below is the plot of potential energy versus internuclear distance (d) of H₂ molecule in the electronic ground state. What is the value of the net potential energy E₀ (as indicated in the figure) in kJ mol^-1, for d = d₀ at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As reference, the potential energy of H atom is taken as zero when its electron and the nucleus are infinitely far apart.
Use Avogadro constant as 6.023 $$ \times $$ 10²³ mol^-1.

Not considering the electronic spin, the degeneracy of the second excited state( n = 3) of H atom is 9, while the degeneracy of the second excited state of H^– is ___________.