InterviewSolution
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InterviewSolution
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At what value of kinetic energy is the de Broglie wavelength of an electron equal to its Compton wavelength? |
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Answer» SOLUTION :The DE Broglie wavelength is `lambda_(DB)=((2 pi ħ)/(m_(0)V))/(sqrt(1-V^(2)//c^(2)))=(2pi ħ)/(m_(0)V)sqrt(1-V^(2)//c^(2))` and the compton wavelength is `lambda_(c )=(2piħ)/(m_(0)c)` The two are equal if `beta=sqrt(1-beta^(2))`, where `beta=(v)/(c )` or `beta=(1)/(sqrt(2))` The CORRESPONDING kinetic energy is `T=(m_(0)c^(2))/(sqrt(1-beta^(2)))-m_(0)c^(2)= (sqrt(2)-1)m_(0)c^(2)` Here `m_(0)` is the rest mass of the particle (here an electron) |
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