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  • Relativistic corrections become necessary when the expression for the kinetic energy 1/2 mv2 , becomes comparable with mc2, where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron?

Relativistic corrections become necessary when the expression for the kinetic energy 1/2 mv2 , becomes comparable with mc2, where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron?

(a)\lambda=10nm\\ (b)\lambda=10^{-1}\\ (c)\lambda=10^{-4}\\ (d)\lambda=10^{-6}\\

Answers (1)

The answer is the option (c, d)
The wavelength of de-Broglie wave is given by
\lambda = h/p = h/mv
Here, h=6.6*10-34
and for electron, m=9*10-31 Kg 

v=\frac{h}{m\lambda}\\ =6.6 * \frac{10^{-34}}{9*10^{-31}\lambda}\\ =6.6*\frac{10^{-34+31}}{9\lambda}=0.73*\frac{10^{-3}}{\lambda}......(i)

(a)\lambda=10nm=10^{-8}m\\ using \; the\; formula\;(i)v=7.3*10^{4}<3*10^{8}\\ (b)\lambda=10^{-1}nm=10^{-10}m\\ v=7.3*10^{6}<10^{8}\\ ({c})\lambda=10^{-4}nm=10^{-13}m\\ v=7.3*10^{9}>10^{8}\\ (d)\lambda=10^{-6}nm=10^{-15}m\\ v=7.3*10^{11}>10^{8}\\

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