The ionization potential of a hydrogen-like atom is $122.4 \, V$. Find its atomic number $Z$.

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

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

In a muonic atom,a muon of mass $200$ times that of an electron and the same charge is bound to a proton. The wavelengths of its Balmer series are in the range of

The energy of an electron in the ground state of a hydrogen atom is $E$. What is the energy of an electron in the $2^{nd}$ excited state of $Li^{++}$?

The velocity of an electron in the second orbit of a sodium atom (atomic number $Z = 11$) is $v$. The velocity of an electron in its fifth orbit will be