Electrons are accelerated through a potential difference V and protons are accelerated through a potential difference 4 V. The de-Broglie wavelengths are λe and λp for electrons and protons respectively. The ratio of (λe)/(λp) is given by: (given me is mass of electron and mp is mass of proton). (a) (λe)/(λp) = √((mp)/(me)) (b) (λe)/(λp) = √((me)/(mp)) (c) (λe)/(λp) = 1/2√((me)/(mp)) (d) (λe)/(λp) = 2√((mp)/(me))

Answer: (d). λ = (h)/(√(2meV)), same charge magnitude. (λe)/(λp) = √((mp(4V))/(meV)) = 2√((mp)/(me)) So the answer is (d).

Electrons are accelerated through a potential difference V and… | JEE Main 2013 (23 Apr, Shift 1)

Q138JEE Main 2013 · 23 APR · SHIFT 1Medium

Matter Waves: de Broglie Wavelength

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).

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Answer: (d)

$\lambda = \dfrac{h}{\sqrt{2meV}}$ , same charge magnitude.
$\dfrac{\lambda_e}{\lambda_p} = \sqrt{\dfrac{m_p(4V)}{m_eV}} = 2\sqrt{\dfrac{m_p}{m_e}}$
So the answer is (d).

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