Hydrogen $(H)$,Deuterium $(D)$,Helium $(He^+)$,and Lithium $(Li^{2+})$ emit radiation of wavelengths $\lambda_1, \lambda_2, \lambda_3,$ and $\lambda_4$ respectively during the transition from $n = 2$ to $n = 1$. Then:

$A$ hydrogen atom at rest emits a photon during its transition from $n = 2$ to $n = 1$. Choose the $INCORRECT$ statement.

The electron in a hydrogen atom is moving in an orbit of radius $0.53 \text{ Å}$. It takes $1.571 \times 10^{-16} \text{ s}$ to complete one revolution. The velocity of the electron will be $[\pi = 3.142]$.

To explain his theory,Bohr used

Ratio of centripetal acceleration for an electron revolving in $3^{\text{rd}}$ orbit and $5^{\text{th}}$ Bohr orbit of hydrogen atom is

$A$ 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 $1/4$
$(3)$ $m=2$
$(4)$ $\Delta p_{a} / \Delta p_{e} = 1/2$