If the radius of the first orbit of a hydrogen atom is $5.29 \times 10^{-11} \, m$,the radius of the fourth orbit will be ......... $\mathring{A}$.

In a hydrogen atom in its ground state,the first Bohr orbit has radius $r_1$. When the atom is raised to one of its excited states,the electron's orbital velocity becomes one-third of its initial value. The radius of that orbit is: (in $r_1$)

For $He^{+}$, a transition takes place from the orbit of radius $105.8 \ pm$ to the orbit of radius $26.45 \ pm$. The wavelength (in $nm$) of the emitted photon during the transition is. . . . .
[Use: Bohr radius, $a_0=52.9 \ pm$; Rydberg constant, $R_H=2.2 \times 10^{-18} \ J$; Planck's constant, $h=6.6 \times 10^{-34} \ J \ s$; Speed of light, $c=3 \times 10^8 \ m \ s^{-1}$]

What is the energy of $He^+$ electron in the first orbit in $eV$?

In the Bohr model of the hydrogen atom,the linear momentum of the electron depends on the principal quantum number $n$ as:

An electron in the hydrogen atom excites from the $2^{nd}$ orbit to the $4^{th}$ orbit. The change in angular momentum of the electron is (Planck's constant $h = 6.64 \times 10^{-34} \ J \cdot s$).