$A$ 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 a hydrogen atom,when an electron transitions from the $4^{th}$ orbit to the $2^{nd}$ orbit,the wave number is $20,397 \, cm^{-1}$. What will be the wave number when an electron in a $He^+$ ion transitions from the $4^{th}$ orbit to the $2^{nd}$ orbit?

$A$ hydrogen atom changes its state from $n=3$ to $n=2$. Due to recoil,the percentage change in the wavelength of emitted light is approximately $1 \times 10^{-n}$. The value of $n$ is . . . . . . .[Given $Rhc=13.6 \text{ eV}, hc=1242 \text{ eV nm}, h=6.6 \times 10^{-34} \text{ J s}$,mass of the hydrogen atom $=1.67 \times 10^{-27} \text{ kg}$]

The radius of the first orbit in a hydrogen atom is $5.3 \times 10^{-11} \text{ m}$. The kinetic energy $E_K$, potential energy $E_P$, and total energy $E_T$ of the electron in the first orbit are:

Which of the plots shown in the figure represents speed $(v)$ of the electron in a hydrogen atom as a function of the principal quantum number $(n)$?

The radius of an electron's second stationary orbit in Bohr's atom is $R$. The radius of the $3rd$ orbit will be $.........R$.