The wavelength of the first Balmer line caused by a transition from the $n=3$ level to the $n=2$ level in hydrogen is $\lambda_1$. The wavelength of the line caused by an electronic transition from $n=5$ to $n=3$ is

Consider the spectral line resulting from the transition $n = 2 \rightarrow n = 1$ in the atoms and ions given below. The shortest wavelength is produced by:

Given below are two statements $:$ one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A :$ The Bohr model is applicable to hydrogen and hydrogen$-$like atoms only.
Reason $R :$ The formulation of Bohr model does not include repulsive force between electrons.
In the light of the above statements,choose the correct answer from the options given below $:$

The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to (where $e, h$ and $c$ have their usual meanings).

Neglecting the reduced mass effect,which optical transition in the $He^+$ spectrum has the same wavelength as the first Lyman transition of hydrogen ($n = 2$ to $n = 1$)?

The gravitational force between a $H$-atom and another particle of mass $m$ is given by Newton's law $F = G\frac{M m}{r^2}$. Here,$M$ represents: