A single electron ion has nuclear chrage `+Ze` where `Z` is atomic number and `e` is electronic charge. It requires `16.52 eV` to excite the electron from the second Bohr orbit to third 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 on first Bohr orbit?

Answer

(a) `Z=3`, (b) `108.8 eV`, (c) `1.013xx10^(-8) m`, (d) `122.4 eV`

Explanation

(a) `16.52=(E_(3)-E_(2))xxZ^(2)`
`16.52=1.89xxZ^(2) rArr Z^(2)=9 "or" Z=3`
(b) `(E_(3)-E_(1))_(z)=12.09xxZ^(2)=12.09xx9=108.81 eV`
(c ) `lambda=12400/(DeltaE_(1 tp oo))=12400/(13.6xx3^(2))=101.3 Å=1.013xx10^(-8) m`,
(d) `KE_(1)=13.6 Z^(2) eV=13.6xx3^(2)=122.4 eV`