The wavelength of a photon emitted by a stationary helium atom is $0.1 \ \mathring{A}$. What is the recoil energy of the atom in $eV$?

$A$ hydrogen atom emits a photon corresponding to an electron transition from $n = 5$ to $n = 1$. The recoil speed of the hydrogen atom is almost......$m/s$ (mass of proton $\approx 1.6 \times 10^{-27} \ kg$).

Match the appropriate pairs from List-$I$ and List-$II$:

List-$I$	List-$II$
$1$. Nitrogen molecules	$(A)$ Continuous spectrum
$2$. Incandescent solids	$(B)$ Absorption spectrum
$3$. Fraunhofer lines	$(C)$ Band spectrum
$4$. Electric arc between iron rods	$(D)$ Emission spectrum

Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge $Ze$ are defined by their principal quantum number $n$,where $n \gg 1$. Which of the following statement$(s)$ is(are) true?
$(A)$ Relative change in the radii of two consecutive orbitals does not depend on $Z$
$(B)$ Relative change in the radii of two consecutive orbitals varies as $1/n$
$(C)$ Relative change in the energy of two consecutive orbitals varies as $1/n^3$
$(D)$ Relative change in the angular momenta of two consecutive orbitals varies as $1/n$

The ionisation energy of an electron in the ground state of a helium atom is $24.6 eV$. The energy required to remove both electrons is: (in $eV$)

Band spectrum is obtained when the source emitting light is in the form of