In a hydrogen-like atom,the velocity of an electron in the second orbit is $v$. What will be the velocity of the electron in its fifth orbit?

The de-Broglie wavelength of an electron in the $n^{th}$ Bohr orbit is $\lambda_n$ and the angular momentum is $J_n$,then:

The ground state energy of a hydrogen atom is $-13.6 \text{ eV}$. What is the ratio of the kinetic energy to the potential energy of the electron in this state?

$A$ stationary hydrogen atom undergoes a transition from $n=5$ to $n=4$. The recoil speed of the atom is (where $R=$ Rydberg constant,$h=$ Planck's constant,and $m=$ mass of the hydrogen atom).

If the energy required to remove one of the two electrons from a $He$ atom is $29.5 \,eV$,then what is the total energy required to convert a helium atom into an $\alpha$-particle (i.e.,$He^{2+}$ ion)?

In a hydrogen-like ion,the energy difference between the $2^{\text{nd}}$ excitation state and the ground state is $108.8 \ eV$. The atomic number of the ion is: