Angular momentum of an electron in a hydrogen atom is $\frac{3h}{2\pi}$. The wavelength of this electron is approximately $...... \mathring{A}$.

The magnitude of acceleration of the electron in the $n$th orbit of a hydrogen atom is $a_{H}$ and that of a singly ionised helium atom is $a_{He}$. The ratio of $a_{H} : a_{He}$ is

The ratio of the velocity of an electron in the ground state of a hydrogen atom to the velocity of light (in $CGS$ units) is:

$A$ small particle of mass $m$ moves in such a way that its potential energy $U = \frac{1}{2} m \omega^2 r^2$,where $\omega$ is a constant and $r$ is the distance of the particle from the origin. Assuming Bohr's quantization of angular momentum and a circular orbit,the radius of the $n^{\text{th}}$ orbit will be proportional to:

In a muonic atom,a muon of mass $200$ times that of an electron and the same charge is bound to a proton. The wavelengths of its Balmer series are in the range of

In the hydrogen atom,the electron makes a transition from the higher orbit $(i)$ to a lower orbit $(f)$. The ratio of the radius of the orbits is given by $r_i : r_f = 16 : 4$. The wavelength of the photon emitted due to this transition is . . . . . . nm. (Given Rydberg constant $R = 1.0973 \times 10^7 \text{ m}^{-1}$)