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JEE Main 2023 (11 Apr, Shift 2) · Matter Waves: de Broglie Wavelength

Matter Waves: de Broglie Wavelength question from JEE Main 2023 (11 Apr, Shift 2)

Q76JEE Main 2023 · 11 APR · SHIFT 2Medium

Matter Waves: de Broglie Wavelength

The ratio of the de-Broglie wavelengths of proton and electron having same Kinetic energy: (Assume $m_p = m_e \times 1849$ )

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Answer: (a)

$\lambda = \dfrac{h}{\sqrt{2mK}}$ ; same $K$ gives $\lambda \propto \dfrac{1}{\sqrt{m}}$ .
$\dfrac{\lambda_p}{\lambda_e} = \sqrt{\dfrac{m_e}{m_p}} = \dfrac{1}{\sqrt{1849}} = \dfrac{1}{43}$
So the answer is (a) $1:43$ .

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