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

$A$ muon is an unstable particle with a mass of $207 \, m_e$ and a charge of either $+e$ or $-e$. $A$ muon $(\mu^-)$ is captured by a hydrogen nucleus to form a muonic atom. If the proton captures the $\mu^-$, find the ionization energy of this atom in $keV$.

An electron in a hydrogen atom makes a transition from $n_1$ to $n_2$. If the time period of the electron in the initial state is eight times that in the final state,then:

The energy required to ionise a hydrogen-like ion in its ground state is $9$ Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state? ........$nm$

Given below are two statements $:$ one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A :$ The Bohr model is applicable to hydrogen and hydrogen$-$like atoms only.
Reason $R :$ The formulation of Bohr model does not include repulsive force between electrons.
In the light of the above statements,choose the correct answer from the options given below $:$

According to de-Broglie, the de-Broglie wavelength for an electron in an orbit of a hydrogen atom is $10^{-9} \, m$. The principal quantum number for this electron is: