The momentum of an electron revolving in the $n^{\text{th}}$ orbit is given by: (Symbols have their usual meanings)

Consider the $3^{rd}$ orbit of $He^{+}$ (Helium) using a non-relativistic approach. The speed of the electron in this orbit will be (given $K = 9 \times 10^9 \; N \cdot m^2/C^2$,$Z = 2$,and $h = 6.6 \times 10^{-34} \; J \cdot s$).

According to Bohr's theory,the expressions for the kinetic and potential energy of an electron revolving in an orbit are given respectively by:

The de-Broglie wavelength of an electron moving in the $n^{\text{th}}$ Bohr orbit of radius $r$ is

The de-Broglie wavelength of the electron in the first Bohr orbit of the hydrogen atom is

In a hydrogen-like atom with atomic number $Z$,an electron is in an excited state with principal quantum number $2n$. The maximum energy of a photon that can be emitted from this state is $204 \ eV$. If the electron transitions from the $2n$ orbit to the $n$ orbit,a photon with energy $40.8 \ eV$ is emitted. The value of $n$ is: