Electrons are accelerated through a potential difference \(V\) and protons are accelerated through a potential difference \(4\, V\). The de-Broglie wavelengths are \(\lambda_e \) and \(\lambda_p \) for electrons and protons respectively. The ratio of \(\frac{{{\lambda _e}}}{{{\lambda _p}}}\) is given by : (given \(m_e\) is mass of electron and \(m_p\) is mass of proton).

1. A \(\frac{{{\lambda _e}}}{{{\lambda _p}}} = \sqrt {\frac{{{m_p}}}{{{m_e}}}} \)
2. B \(\frac{{{\lambda _e}}}{{{\lambda _p}}} = \sqrt {\frac{{{m_e}}}{{{m_p}}}} \)
3. C \(\frac{{{\lambda _e}}}{{{\lambda _p}}} = \frac{1}{2}\sqrt {\frac{{{m_e}}}{{{m_p}}}} \)
4. D \(\frac{{{\lambda _e}}}{{{\lambda _p}}} = 2\sqrt {\frac{{{m_p}}}{{{m_e}}}} \)