According to Bohr's theory,the radius of an electron in an orbit described by principal quantum number $n$ and atomic number $Z$ is proportional to:

The energy required to remove the electron from a singly ionized Helium atom is $2.2$ times the energy required to remove an electron from a Helium atom. The total energy required to ionize the Helium atom completely is......$eV$

The following parameter is the same for all hydrogen-like atoms and ions in their ground state.

According to Bohr's theory,the expressions for the kinetic and potential energy of an electron revolving in an orbit are given respectively by:

$A$ particle of mass $200 \, MeV/c^2$ collides with a hydrogen atom at rest. Soon after the collision,the particle comes to rest,and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in $eV$) is $\frac{N}{4}$. The value of $N$ is: (Given the mass of the hydrogen atom to be $1 \, GeV/c^2$)

Magnetic field at the centre of the hydrogen atom due to the motion of an electron in the $n^{\text{th}}$ orbit is proportional to: