The de Broglie wavelength of an electron revolving in the first Bohr orbit of circumference $2\pi r$ is ............

Using the Bohr model,calculate the electric current created by the electron when the $H$-atom is in the ground state.

An electron is moving in an orbit of a hydrogen atom from which there can be a maximum of six transitions. An electron is moving in an orbit of another hydrogen atom from which there can be a maximum of three transitions. The ratio of the velocities of the electron in these two orbits is

Minimum excitation potential of Bohr's first orbit in hydrogen atom is.....$V$

$A$ doubly charged lithium atom $(Li^{++})$ is a hydrogen-like species with atomic number $Z = 3$. The wavelength of the radiation required to excite an electron from the first to the third Bohr orbit in $Li^{++}$ is.......$\mathring{A}$ (Ionization energy of hydrogen atom is $13.6\,eV$).

In the hydrogen atom, the electron makes a transition from the higher orbit $(i)$ to a lower orbit $(f)$. The ratio of the radius of the orbits is given by $r_i : r_f = 16 : 4$. The wavelength of the photon emitted due to this transition is . . . . . . nm. (Given Rydberg constant $R = 1.0973 \times 10^7 \text{ m}^{-1}$)