The orbital acceleration of an electron in a hydrogen atom is given by:

The radius of the fifth orbit of the $Li^{++}$ ion is $......... \times 10^{-12} \ m$. Take: radius of the hydrogen atom (first Bohr radius) $r_0 = 0.51 \ \mathring{A}$.

Find the ratio of the area of the orbit of the first excited state to the ground state in a hydrogen atom.

The angular momentum of an electron in Bohr's hydrogen atom having energy $(-0.544) \text{ eV}$ is ($h$ = Planck's constant)

$A$ $15.0\, eV$ photon collides with and ionizes a hydrogen atom. If the atom was originally in the ground state (ionization potential $= 13.6\, eV$),what is the kinetic energy of the ejected electron? .......... $eV$

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,