In a hydrogen-like ion,the energy difference between the $2^{\text{nd}}$ excitation state and the ground state is $108.8 \ eV$. The atomic number of the ion is:

$A$ particle of mass $m$ moves in a circular orbit in a central potential field $U(r) = U_{0}r^{4}$. If Bohr's quantization conditions are applied,the radii of possible orbitals $r_{n}$ vary with $n^{1/\alpha}$,where $\alpha$ is ....... .

Suppose in a hypothetical world, the angular momentum is quantized to be even integral multiples of $\frac{h}{2 \pi}$. According to Bohr's model, what will be the largest possible wavelength emitted by hydrogen atoms in the visible range in this world (in $\text{ nm}$)? (Consider $hc = 1242 \text{ eV-nm}$)

When a hydrogen atom,initially at rest,emits a photon resulting in a transition $n = 5 \rightarrow n = 1$,its recoil speed is about

An ionic atom equivalent to a hydrogen atom has a wavelength equal to $1/4$ of the wavelength of the corresponding hydrogen line. The ion is:

If the radius of the first Bohr orbit in a hydrogen atom is $0.53 \, \mathring A$,then the radius of the third Bohr orbit will be ....... $\mathring A$.