If one takes into account the finite mass of the proton,then the correction to the binding energy of the hydrogen atom is approximately (take,mass of proton $= 1.60 \times 10^{-27} \, kg$ and mass of electron $= 9.10 \times 10^{-31} \, kg$) (in $\%$)

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

When the electron orbiting in a hydrogen atom in its ground state moves to the third excited state,the de-Broglie wavelength associated with it

In Bohr's model of hydrogen-like species,which of the following is true?

If an electron is moving in the $n^{\text{th}}$ orbit of the hydrogen atom,then its velocity $(v_n)$ for the $n^{\text{th}}$ orbit is given as:

$A$ free hydrogen atom after absorbing a photon of wavelength $\lambda_{a}$ gets excited from the state $n=1$ to the state $n=4$. Immediately after that,the electron jumps to $n=m$ state by emitting a photon of wavelength $\lambda_{e}$. Let the change in momentum of the atom due to the absorption and the emission be $\Delta p_{a}$ and $\Delta p_{e}$,respectively. If $\lambda_{a} / \lambda_{e} = 1/5$,which of the following options is/are correct?
[Use $hc = 1242 \text{ eV nm}$; $1 \text{ nm} = 10^{-9} \text{ m}$,$h$ and $c$ are Planck's constant and speed of light,respectively]
$(1)$ $\lambda_{e} = 418 \text{ nm}$
$(2)$ The ratio of kinetic energy of the electron in the state $n=m$ to the state $n=1$ is $1/4$
$(3)$ $m=2$
$(4)$ $\Delta p_{a} / \Delta p_{e} = 1/2$