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The energy that should be added to an el...

The energy that should be added to an electron to reduce its de-Broglie wavelength from 1 nm to 0.5 nm is

A

four times the initial energy

B

equal to the initial energy

C

twice the initial energy

D

thrice the initial energy

Text Solution

Verified by Experts

The correct Answer is:
D
de-Broglie wavelength,
`lambda=(h)/sqrt(2mE)`
`(lambda_(1))/(lambda_(2))=sqrt((E_(2))/(E_(1)))`
` implies " "(1xx10^(-9))/(0.5 xx 10^(-9))=sqrt((E_(2))/(E_(1)))`
`implies " "2=sqrt((E_(2))/(E_(1)))`
`implies " "E_(2)/(E_(1))=4`
`therefore" "E_(2)=4E_(1)`
`therefore` Energy to be added `=E_(2)-E_(1)=4E_(1)-E_(1)=3E_(1)`
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