A 100 eV electron collides with a stationary helium ion (He + ) in its ground state and exits to a higher level. After the collision, He + ions emits two photons in succession with wavelength 1085 Å and 304 Å. Calculate the energy of the electron after the collision (in 10 –1 eV). Given h = 6.63 × 10 –34 Js.
Text Solution
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The energy of the electron in the 
state of 
ion of atomic number Z is given by
for 
ion 
. Therefore
The energies 
and 
of the two emitted photons in eV are
Thus total energy 
Let 
be the principle quantum number of exited state. Now we have for the transition from 
to 
But 
. Therefore 
Which gives 
or 
The energy of the incident electron 
(given). The energy supplied to 
ion 
.
Therefore, the energy of the electrons left after the collision 
.
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