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A proton of mass '\({m}_{p}\)' has same energy as that of a photon of wavelength '\(\lambda\)'. If the proton is moving …

Q1

A proton of mass '\({m}_{p}\)' has same energy as that of a photon of wavelength '\(\lambda\)'. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.

[JEE Main 2025, 28 Jan (Shift 1)]

a

\begin{equation}
\frac{1}{c} \sqrt{\frac{E}{m_p}}
\end{equation}

b

\begin{equation}
\frac{1}{c} \sqrt{\frac{E}{2 m_p}}
\end{equation}

c

\begin{equation}
\frac{1}{c} \sqrt{\frac{2 \mathrm{E}}{\mathrm{~m}_{\mathrm{p}}}}
\end{equation}

d

\begin{equation}
\frac{1}{2 c} \sqrt{\frac{\mathrm{E}}{\mathrm{~m}_{\mathrm{p}}}}
\end{equation}

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