The energy that should be added to an electron, to reduce its de-Broglie wavelengths from `10^(-10) m` to `0.5 xx 10^(-10)` m wil be

Options

A. four times the initial energy
B. thrice the initial energy
C. equal to the initial energy
D. twice the initial energy

Answer

B

Explanation

As `lamda=(h)/(sqrt(2mE)) implies lamda prop (1)/(sqrt(E))`
or `(lamda_(1))/(lamda_(2))=sqrt((E_(2))/(E_(1)))`
`implies (10^(-10))/(0.5xx10^(-10))=sqrt((E_(2))/(E_(1)))`
`implies E_(2)=4E_(1)`
therefore, added energy `=E_(2)-E_(1)=3E_(1)`.