Let r be the radius of the uniform circular motion of the electron. The electric field intensity \(\vec E\) at every point on the circular path is radially outward and has the same magnitude E = \(\cfrac{λ}{2πεr}\).
∴ The centripetal force on the electron,
where me and v are the mass and linear speed of the electron.
∴ mev2 = \(\cfrac{eλ}{2πε}\)
∴ The kinetic energy of the electron,
\(\cfrac12\) mev2 = \(\cfrac{eλ}{4πε}\)