The force acting on the electron in a hydrogen atom (Bohr's theory) is related to the principal quantum number $n$ as:

Find the energy of the third stationary orbit of Bohr's model of the hydrogen atom if the energy of the ground state is $-E \text{ J}$.

$A$ muon $(\mu^-)$ is a negatively charged particle $(|q| = |e|)$ with a mass $m_{\mu} = 200 m_e$,where $m_e$ is the mass of the electron and $e$ is the elementary charge. If a $\mu^-$ is bound to a proton to form a hydrogen-like atom,identify the correct statements:
$(A)$ The radius of the muonic orbit is $200$ times smaller than that of the electron.
$(B)$ The speed of the $\mu^-$ in the $n^{th}$ orbit is $\frac{1}{200}$ times that of the electron in the $n^{th}$ orbit.
$(C)$ The ionization energy of the muonic atom is $200$ times more than that of a hydrogen atom.
$(D)$ The momentum of the muon in the $n^{th}$ orbit is $200$ times more than that of the electron.

Assuming the atom in the ground state,the expression for the magnetic field at a point (nucleus) in a hydrogen atom due to the circular motion of the electron is [$\mu_{0} =$ permeability of free space,$\epsilon_{0} =$ permittivity of free space,$m =$ mass of electron,$e =$ electronic charge,$h =$ Planck's constant].

The figure shows a graph between $\ln \left| \frac{A_n}{A_1} \right|$ and $\ln |n|$, where $A_n$ is the area enclosed by the $n^{th}$ orbit in a hydrogen-like atom. The correct curve is

Energy levels $A, B, C$ of a certain atom correspond to increasing values of energy,i.e.,$E_A < E_B < E_C$. If $\lambda_1, \lambda_2, \lambda_3$ are the wavelengths of radiations corresponding to the transitions $C$ to $B$,$B$ to $A$,and $C$ to $A$ respectively,which of the following statements is correct?