Find the energy that should be added to an electron of energy 2eV to reduce its de-Broglie wavelength from 1nm to 0.5nm.

Explanation

As `lambda=h/(sqrt(2mE_(K)))` or `E_(K)=(h^(2))/(2mlambda^(2))`
or `E_(K) prop1/(lambda^(2))`
`:. (E_(K_(1)))/(E_(K_(2)))=[(lambda_(2))/(lambda_(1))]^(2)=[0.5/1]^(2)=1/4`
or `E_(K_(2))=4E_(K_(1))=4xx2eV=8eV`
Increases in energy `=E_(K_(2))-E_(K_(1))=8-2=6 eV`