At what value of kinetic energy is the de Broglie wavelength of an electron equal to its Compton wavelength?

Explanation

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)