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)?

The ratio of the area of the first excited state to the ground state orbit of a hydrogen atom is:

$A$ hydrogen atom is in its $n^{\text{th}}$ energy state. If the de-Broglie wavelength of the electron is $\lambda$,then:

The potential energy of a proton and an electron in a hydrogen atom is given by $V = V_0 \ln \left( \frac{r}{r_0} \right)$,where $r_0$ is a constant. Assuming the system follows the Bohr model,find the relationship between the radius $r_n$ and the principal quantum number $n$.

The radius of the first permitted Bohr orbit for the electron in a hydrogen atom equals $0.53 \mathring{A}$ and its ground state energy equals $-13.6 \; eV$. If the electron in the hydrogen atom is replaced by a muon $(\mu^{-})$ [charge same as electron and mass $207 m_{e}$], the first Bohr radius and ground state energy will be:

In any Bohr orbit of the hydrogen atom,the ratio of kinetic energy to potential energy of the electron is