The energy levels of hypothetical one electron atom are shown below
`e"____"n=oo`
`-0.50eV"_____"n=5`
`-1.45eV"_____"n=4`
`-3.08eV"____"n=3`
`-5.3eV"____"n=2`
`-15.6eV"____"n=1`

Options

A. Find the ionisation potential of atom?
B. Find the short wavelength limit of the series terminating at `n=2`?
C. Find the wave no. of photon emitted for the transition made by the electron from third orbit to first orbit ?
D. Find the minimum energy that an electron will have after interacting with this atom in the ground state, if the initial kinetic energy of the electron is (i) 6eV (ii) eV ?

Answer

A, B, C, D

Explanation

(a) `I.P. =overset(DeltaE)(1=oo) =E_(oo) -E_(1)=0-(-15.6)=15.6.l.v`.
(b) `n=oo" "n=2`
`DeltaE = [0-(-5.3)]=5.3l.v`.
`DeltaE =(1240)/(lambda(nm))" "lambda=(1240)/(5.3)=233.9nm`
`(c ) |DeltaE_(3rarr1)|=|-3.08-(-15.6)|=15.6-3.08=12.52l.v.=(1240)/(lambda)=(12.52)/(1240)=(1)/(lambda)(n.m)`
`lambda = 1.808xx10^(7)m^(-1)`
(d) (i)`E=-15.6-(-6)=-15.6+6=-9.6`
(ii) `E=-15.6-(-11)=-15.6+11=-4.6`