The de-Broglie wavelength of the electron in the ground state of a hydrogen atom is ........ $\mathring{A}$.

The wavelength of the radiation emitted is $\lambda_0$ when an electron jumps from the second excited state to the first excited state of a hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be $(20\lambda_0/x)$. The value of $x$ is

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 $:$

$A$ hydrogen atom changes its state from $n=3$ to $n=2$. Due to recoil,the percentage change in the wavelength of emitted light is approximately $1 \times 10^{-n}$. The value of $n$ is . . . . . . .[Given $Rhc=13.6 \text{ eV}, hc=1242 \text{ eV nm}, h=6.6 \times 10^{-34} \text{ J s}$,mass of the hydrogen atom $=1.67 \times 10^{-27} \text{ kg}$]

The magnetic moment $(m_{orb})$ of a revolving electron around the nucleus varies with the principal quantum number $(n)$ as

Suppose an electron in an atom experiences an attractive force towards the nucleus given by $F = k/r$,where $k$ is a constant and $r$ is the distance of the electron from the nucleus. Applying the Bohr model to this system,the radius of the $n^{th}$ orbit $r_n$ and the kinetic energy of the electron in that orbit $K_n$ are found. Which of the following relationships is correct?