\(\frac{ h }{ p _{ e }}=\frac{ h }{ p _{ ph }}\)

\(\sqrt{2 mk _{ e }}=\frac{ E _{ ph }}{ c }\)

\(2 mk _{ e }=\frac{\left( E _{ ph }\right)^{2}}{ c ^{2}}\)

\(\frac{ k _{ e }}{ E _{ ph }}=\frac{ E _{ ph }}{ c ^{2}}\left(\frac{1}{2 m }\right)\)

\(=\frac{ p _{ ph }}{ c }\left(\frac{1}{2 m }\right)\)

\(=\frac{ p _{ e }}{ c }\left(\frac{1}{2 m }\right)\)

\(=\frac{ mv }{ c } \frac{1}{2 m }\)

\(=\frac{V}{2 c}\)