Monochromatic radiation of wavelength $\lambda$ is incident on a hydrogen sample containing atoms in the ground state. Hydrogen atoms absorb the light and subsequently emit radiations of ten different wavelengths. The value of $\lambda$ is.....$nm$.

If the radius of a hydrogen atom in its first orbit is $a_{0}$,then its radius in the third excited state is . . . . . . . (in $a_{0}$)

$A$ particular hydrogen-like ion emits radiation of frequency $3 \times 10^{15} \,Hz$ when it makes a transition from $n=2$ to $n=1$. The frequency of radiation emitted in a transition from $n=3$ to $n=1$ is $\frac{x}{9} \times 10^{15} \,Hz$, where $X = \text{ . . . . . . }$.

The de-Broglie wavelength of an electron in the first Bohr orbit is

To which of the following is the angular velocity of the electron in the $n$-th Bohr orbit proportional?

The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is