The Bohr model of atoms:

What is ionisation energy?

Four electrons,each of mass $m_{e}$,are in a one-dimensional box of size $L$. Assume that the electrons are non-interacting,obey the Pauli exclusion principle,and are described by standing de Broglie waves confined within the box. Define $\alpha = h^{2} / 8 m_{e} L^{2}$ and $U_{0}$ to be the ground state energy. Then,

Using Bohr's atomic model, the orbital period of an electron in a hydrogen atom in the $n^{th}$ orbit is ($\epsilon_0$ = permittivity of free space, $h$ = Planck's constant, $m$ = mass of electron, $e$ = electronic charge).

The kinetic energy of the electron in an orbit of radius $r$ in a hydrogen atom is proportional to ($e$ = electronic charge).

In the Bohr model of a hydrogen atom,the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If ${a_0}$ is the radius of the ground state orbit,$m$ is the mass,$e$ is the charge on the electron,and ${\varepsilon _0}$ is the vacuum permittivity,the speed of the electron is: