When an electron jumps from the orbit $n=2$ to $n=4$,the wavelength of the radiation absorbed will be ($R$ is Rydberg's constant).

The de Broglie wavelength of an electron in the first orbit of Bohr's model is . . . . . . .

According to the de Broglie hypothesis,if the de Broglie wavelength of an electron in a hydrogen atom orbit of radius $5.3 \times 10^{-11} \ m$ is $10^{-10} \ m$,then the principal quantum number of the electron 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 number of absorption transitions between the first and the fourth energy states of a hydrogen atom is $3$. The number of emission transitions between these states will be

The product of angular speed and tangential speed of an electron in the $n^{\text{th}}$ orbit of a hydrogen atom is: