Consider a hydrogen atom with $v_k, r_k,$ and $K_k$ denoting the velocity, orbital radius and kinetic energy of the electron in the $k^{{th}}$ orbit, respectively. The electron undergoes a transition from the $n^{{th}}$ orbit, emitting radiation corresponding to the Lyman series. Considering $h$ to be the Planck’s constant and $ ho_0$ the permittivity of the free space, the correct statement(s) is/are:

A particle of mass $m$ is moving in a circular orbit under the influence of the central force $F(r)=-k r$, corresponding to the potential energy $V(r)=k r^2 / 2$, where $k$ is a positive force constant and $r$ is the radial distance from the origin. According to the Bohr's quantization rule, the angular momentum of the particle is given by $L=n \hbar$, where $\hbar=h /(2 \pi), h$ is the Planck's constant, and $n$ a positive integer. If $v$ and $E$ are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_{b}^{p}$ and the binding energy of a neutron be $E_{b}^{n}$ in the nucleus.

Which of the following statement(s) is(are) correct?