Apply Bohr's atomic model to a lithium atom. Assuming that its two $K$-shell electrons are so close to the nucleus that the nucleus and the $K$-shell electrons act as a core with an effective positive charge equivalent to $1e$. The ionization energy of its outermost electron is......$eV$.

In which of the following systems will the radius of the first orbit $(n = 1)$ be minimum?

Find the radius of $Be^{3+}$ ions in its ground state assuming Bohr's model to be valid $(a_0 = 53 \ pm)$. (in $pm$)

$A$ hydrogen atom,a deuteron atom,a $He^+$ ion,and a $Li^{++}$ ion each contain a single electron orbiting their nucleus. The wavelengths of the electromagnetic radiation emitted during the transition of the electron from the $n = 2$ orbit to the $n = 1$ orbit are found to be $\lambda_1, \lambda_2, \lambda_3$,and $\lambda_4$ respectively. Then:

$A$ stationary hydrogen atom undergoes a transition from $n=5$ to $n=4$. The recoil speed of the atom is (where $R=$ Rydberg constant,$h=$ Planck's constant,and $m=$ mass of the hydrogen atom).

The radius of the first orbit of hydrogen is $r_{H}$,and the energy in the ground state is $-13.6 \text{ eV}$. Considering a $\mu^{-}$-particle with a mass $207 m_e$ revolving around a proton as in a hydrogen atom,the energy and radius of the proton and $\mu^{-}$-combination respectively in the first orbit are (assume the nucleus to be stationary):