The radius of an electron's second stationary orbit in Bohr's atom is $R$. The radius of the $3rd$ orbit will be $.........R$.

In the $n^{\text{th}}$ Bohr orbit,the ratio of the kinetic energy of an electron to the total energy of it is:

$(a)$ Using the Bohr model,calculate the speed of the electron in a hydrogen atom in the $n = 1, 2,$ and $3$ levels.
$(b)$ Calculate the orbital period in each of these levels.

The radius of the first Bohr orbit is $r$. What is the radius of the $2^{nd}$ Bohr orbit?

The ratio of wavelengths for the transition of electrons from the $2^{nd}$ orbit to the $1^{st}$ orbit of Helium $(He^+)$ and Lithium $(Li^{++})$ is (Atomic number of Helium = $2$,Atomic number of Lithium = $3$).

To calculate the size of a hydrogen ion $(H^-)$ using the Bohr's model,we assume that its two electrons move in an orbit such that they are always on diametrically opposite sides of the nucleus. With each electron having the angular momentum $\hbar = h / 2\pi$ and taking electron interaction into account,the radius of the orbit in terms of the Bohr's radius of hydrogen atom $a_B = \frac{4\pi\varepsilon_0\hbar^2}{me^2}$ is