The radius of the smallest electron orbit in a hydrogen-like ion is $(0.51/4 \times 10^{-10}) \text{ m}$. This ion is:

Given below are two statements.
Statement $(I) :$ The dimensions of Planck's constant and angular momentum are same.
Statement $(II) :$ In Bohr's model,electrons revolve around the nucleus only in those orbits for which angular momentum is an integral multiple of Planck's constant.
In the light of the above statements,choose the most appropriate answer from the options given below.

For an electron moving in the $n^{\text{th}}$ Bohr orbit,the de Broglie wavelength of the electron is:

An electron in a hydrogen atom makes a transition from $n_1$ to $n_2$. If the time period of the electron in the initial state is eight times that in the final state,then:

According to Bohr's model, the radius of the second orbit of a helium ion $(He^+)$ is ........ $\mathring{A}$.

Match the following List-$I$ with List-$II$ in connection with Bohr's atomic model.

$A$. Speed of revolution of electron	$i$. $\frac{1}{4 \pi \varepsilon_0} \frac{2 \pi Z e^2}{n h}$
$B$. Kinetic energy	$ii$. $-\left(\frac{1}{4 \pi \varepsilon_0}\right)^2 \frac{2 \pi^2 m e^4 Z^2}{n^2 h^2}$
$C$. Total energy	$iii$. $\left(\frac{1}{4 \pi \varepsilon_0}\right)^2 \frac{2 \pi^2 m e^4 Z^2}{n^2 h^2}$
$D$. Frequency	$iv$. $\left(\frac{1}{4 \pi \varepsilon_0}\right)^2 \frac{4 \pi^2 Z^2 e^4 m}{n^3 h^3}$