Relativistic corrections become necessary when the expression for the kinetic energy `(1)/(2)mv^(2)`,
becomes comparable with `mc^(2)`,where m is the mass of the particle.At what de-Broglie wavelength will realtivistic corrections become important for an electron?

Options

A. `lambda`=10 nm
B. `labda=10^(-1)`nm
C. `lambda=10^(-4)` nm
D. `lambda=10^(-6)nm`

Answer

C, D

Explanation

Suppose the maximum speed of electron is `v_(max)=c` and its de-Broglie wavelength is `lambda` Its value is ,
`lambda_(min)=(h)/(mv_(max))=(h)/(mc)` ………(1)
`therefore lambda_(min)=(6.625xx10^(-34))/(9.1xx10^(-31)xx3xx10^(8))` `=0.002427xx10^(-9)m`
`therefore lambda_(min)=0.002427`nm ........(2)
`implies` From equations (1) and (2) , we can that if `vgtc` then `lambda ltlambda_(min)`
Here in options (C )and (D) ,we are given `lambdaltlambda_(min)`.Hence in these two cases we get `vgtC`.
Hence in these two cases,we would require to make correction based upon theory of relativity.