Assertion $(A)$: The magnetic moment $(\mu)$ of an electron revolving around the nucleus decreases with increasing principal quantum number $(n)$.
Reason $(R)$: Magnetic moment of the revolving electron,$\mu \propto n$.

If the difference between $(n + 1)^{th}$ Bohr radius and $n^{th}$ Bohr radius is equal to the $(n - 1)^{th}$ Bohr radius, then the value of $n$ is:

$A$ 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.

The potential energy of a proton and an electron in a hydrogen atom is given by $V = V_0 \ln \left( \frac{r}{r_0} \right)$,where $r_0$ is a constant. Assuming the system follows the Bohr model,find the relationship between the radius $r_n$ and the principal quantum number $n$.

If $\lambda_1$ and $\lambda_2$ denote the wavelengths of de Broglie waves for electrons in the first and second Bohr orbits in a hydrogen atom,then $\lambda_1/\lambda_2$ is equal to

Hydrogen $(_1H^1)$,Deuterium $(_1H^2)$,singly ionized Helium $(_2He^4)^+$,and doubly ionized Lithium $(_3^6Li)^{++}$ all have one electron around the nucleus. Consider an electron transition from $n = 2$ to $n = 1$. If the wavelengths of emitted radiation are $\lambda_1, \lambda_2, \lambda_3$,and $\lambda_4$ respectively,then approximately which one of the following is correct?