A particle moving with kinetic energy `E_(1)` has de Broglie wavelength `lambda_(1)`. Another particle of same mass having kinetic energy `E_(2)` has de Broglie wavelength `lambda_(2). lambda_(2)= 3 lambda_(2)`. Then `E_(2) - E_(1)` is equal to

Options

A. `7E_(1)`
B. `3E_(1)`
C. `8E_(1)`
D. `9E_(1)`

Explanation

`p_(1) =( h )/( lambda_(1)) rArr E_(1) =( p_(1)^(2))/( 2m ) rArr E_(1) =( h^(2))/( 2m lambda_(1)^(2)) rArr E_(2) = ( h^(2))/( 2m lambda_(2)^(2)) = ( 9h^(2))/( 2m lambda_(1)^(2)) rArr E_(2) - E_(1) = ( 8h^(2))/( 2 m lambda_(1)^(2)) = 8 E_(1)`