An electron, a doubly ionized helium ion \(\left( He ^{++}\right)\) and a proton are having the same kinetic energy. The relation between their respective de\(-\)Broglie wavelengths \(\lambda_{ e }, \lambda_{ He ^{++}}\) and \(\lambda_{ P }\) is

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(D) \(\lambda_{e}>\lambda_{P}>\lambda_{H e^{++}}\)

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\(\lambda=\frac{ h }{ P }=\frac{ h }{\sqrt{2 m ( KE )}}\)

\(\lambda \propto \frac{1}{\sqrt{ m }} \Rightarrow \lambda=\frac{ C }{\sqrt{ m }}\)

\(m _{ He ^{++}}> m _{ P }> m _{ e }\)

\(\therefore \lambda_{ He ^{++}}<\lambda_{ P }<\lambda_{ e }\)

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