Question

A single electron ion has nuclear charge $+Ze$ where $Z$ is atomic number and $e$ is electronic charge. It requires $16.52eV$ to excite the electron from the second Bohr orbit. Find
(a) The atomic number of element?
(b) The energy required for transition of electron from first to third orbit?
(c) Wavelength of photon required to remove electron from first Bohr orbit to infinity?
(d) The kinetic energy of electron in first Bohr orbit?

Answer 1

Position is $n_1=2⟶n_2=3$
$:\Delta \epsilon =47.2eV$
we have $\Delta \epsilon =13.6z^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})eV$
$47.2=13.6z^2(\frac{1}{2^2}-\frac{1}{3^2})$
$z=5$
5 is the atomic number of the element.