To change de-Broglie wavelength from `0.5xx10^(10)m` to `1xx10^(-10)m` its energy should be……

Options

A. half of initial kinetic energy
B. double of initial kineric energy
C. four times initial kinetic energy
D. `(1)/(4)` times initial kinetics energy

Answer

D

Explanation

`lambda=(h)/(mv)=(h)/(p)`
but p =`sqrt(2mK)`
`therefore` In `lambda=(h)/(sqrt(2mK)),(h)/(sqrt(2m))` same
`therefore lambda prop (1)/(sqrt(K))`
`therefore K prop (1)/(lambda^(2))`
`therefore (K_(2))/(K_(1))=((lambda_(1))/(lambda_(2)))^(2)`
`=((0.5xx10^(-10))/(1xx10^(-10)))=((1)/(2))^(2)=(1)/(4)`
` therefore K_(2)=(K_(1))/(4)`