The ratio of the radius of the second orbit of $Li^{2+}$ to that of the third orbit of $Be^{3+}$ is:

The energy of an electron in the excited hydrogen atom is $-3.4 \ eV$. Then according to Bohr's theory,the angular momentum of the electron in that excited state is ($h=$ Planck's constant).

Light of frequency $1.6 \times 10^{16} \ Hz$ falling on a metal plate emits electrons that have double the kinetic energy compared to the kinetic energy of electrons emitted when light of frequency $1.0 \times 10^{16} \ Hz$ falls on the same plate. The threshold frequency $(v_0)$ of the metal in $Hz$ is:

State whether the following statements are true or false:
$(i)$ In Rutherford's atomic model,the Coulombic forces between the nucleus and electrons are mathematically similar to the gravitational forces $F = G \frac{m_1 m_2}{r^2}$.
$(ii)$ Out of every $20000$ $\alpha$-particles,$\sim 10$ particles bounce back after hitting the gold foil.
$(iii)$ In Rutherford's experiment,a zinc sulfide $(ZnS)$ fluorescent screen is placed around the gold foil.
$(iv)$ Rutherford's $\alpha$-particle scattering experiment is related to the size of the atomic nucleus.

The distance between the $3^{rd}$ and $2^{nd}$ Bohr's orbits in the hydrogen atom is

Bohr’s atomic theory gave the idea of :