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JEE Main 2019 (12 Jan, Shift 1) · Matter Waves: de Broglie Wavelength

Matter Waves: de Broglie Wavelength question from JEE Main 2019 (12 Jan, Shift 1)

Q122JEE Main 2019 · 12 JAN · SHIFT 1Medium

Matter Waves: de Broglie Wavelength

A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass ' 4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths $\frac{\lambda_A}{\lambda_B}$ is close to:

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Answer: (c)

$\lambda = \dfrac{h}{\sqrt{2mqV}}$ , same charge $q$ .
$\dfrac{\lambda_A}{\lambda_B} = \sqrt{\dfrac{m_BV_B}{m_AV_A}} = \sqrt{\dfrac{4m \times 2500}{m \times 50}} = \sqrt{200}$
$\sqrt{200} \approx 14.14$
So the answer is (c) 14.14.

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