The frequency of the light emitted when an electron transitions from the $n=4$ to $n=2$ level in a hydrogen atom is $\frac{3}{7}$ times the frequency of a transition in a $Li^{2+}$ ion. Which transition in the $Li^{2+}$ ion corresponds to this?

In the lowest energy level of a hydrogen atom,the electron has an angular momentum of:

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

Which of the following statements are true regarding Bohr's model of the hydrogen atom?
$(I)$ Orbiting speed of the electron decreases as it shifts to discrete orbits away from the nucleus.
$(II)$ Radii of allowed orbits of the electron are proportional to the principal quantum number.
$(III)$ Frequency with which the electron orbits around the nucleus in discrete orbits is inversely proportional to the cube of the principal quantum number.
$(IV)$ Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbits.
Select the correct answer using the codes given below.

$A$ moving Hydrogen atom makes a head-on collision with a stationary Hydrogen atom. Before the collision,both atoms are in the ground state,and after the collision,they move together. The minimum kinetic energy of the moving Hydrogen atom,such that one of the atoms reaches the excitation state,is (in $eV$)

If the energy of a hydrogen atom in the $n^{th}$ orbit is ${E_n}$,then the energy in the $n^{th}$ orbit of a singly ionized helium atom will be: