Consider a hydrogen atom with its electron in the $n^{\text{th}}$ orbital. An electromagnetic radiation of wavelength $90 \ nm$ is used to ionize the atom. If the kinetic energy of the ejected electron is $10.4 \ eV$,then the value of $n$ is $(hc = 1242 \ eV \ nm)$.

If the difference between the $(n+1)^{\text{th}}$ Bohr radius and the $n^{\text{th}}$ Bohr radius is equal to the $(n-1)^{\text{th}}$ Bohr radius,then find the value of $n$.

$A$ 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 $13.6\,eV$).

Which of the following is an integral multiple of $h/2\pi$ in Bohr's model of a hydrogen atom?

Explain the quantization of angular momentum by considering the electron as a wave in an atom.

If the radius of a hydrogen atom in its first orbit is $a_{0}$,then its radius in the third excited state is . . . . . . . (in $a_{0}$)