The de Broglie wavelengths of a proton and an α particle are λ and 2λ respectively. The ratio of the velocities of proton and α particle will be: (a) 8: 1 (b) 1: 2 (c) 1: 8 (d) 4: 1

Answer: (a). λ = h/mv ⇒ v = (h)/(mλ). (vp)/(vα) = (mα λα)/(mp λp) = (4mp · 2λ)/(mp · λ) = 8 So the answer is (a) 8: 1.

The de Broglie wavelengths of a proton and an α particle are λ and 2λ… | JEE Main 2024 (1 Feb, Shift 1)

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Matter Waves: de Broglie Wavelength

The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2\lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be:

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Answer: (a)

$\lambda = \dfrac{h}{mv} \Rightarrow v = \dfrac{h}{m\lambda}$ .
$\dfrac{v_p}{v_\alpha} = \dfrac{m_\alpha \lambda_\alpha}{m_p \lambda_p} = \dfrac{4m_p \cdot 2\lambda}{m_p \cdot \lambda} = 8$
So the answer is (a) $8 : 1$ .

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