Magnetic moment due to the motion of the electron in the $n$th energy state of a hydrogen atom is proportional to ..........

The de-Broglie wavelength associated with the electron in the $n = 4$ level is

An electron in a hydrogen atom is replaced by an identically charged particle,a muon,with a mass $207$ times that of an electron. What will be the radius of the $K$ shell?

$A$ 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.

If an electron in a hydrogen atom jumps from the third orbit to the second orbit,the frequency of the emitted radiation is given by (where $c$ is the speed of light and $R$ is the Rydberg constant):

For an electron moving in the $n^{\text{th}}$ Bohr orbit,the de Broglie wavelength of the electron is: