If the atom $_{100}Fm^{257}$ follows the Bohr model and the radius of the outermost shell of $_{100}Fm^{257}$ is $n$ times the Bohr radius,then find $n$.

The triply ionized beryllium $(Be^{3+})$ has the same electron orbital radius as that of the ground state of hydrogen. Hence, the energy state of triply ionized beryllium is (Given $Z = 4$ for beryllium)

The de-Broglie wavelength of an electron in the ground state of the hydrogen atom 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 $hc = 1242 \text{ eV-nm}$)

In the Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at $10.2 \, V$. The wavelength of light emitted by the hydrogen atom when excited to the first excitation level is $\qquad$ $nm$.
(Given $hc = 1245 \, eV \cdot nm$, $e = 1.6 \times 10^{-19} \, C$).

In the following atoms and molecules,for the transition from $n = 2$ to $n = 1$,the spectral line of minimum wavelength will be produced by: