If the de Broglie wavelengths associated with a proton and an α -particle are equal, then the ratio of velocities of the proton and the α -particle will be: (a) 4: 1 (b) 2: 1 (c) 1: 2 (d) 1: 4

Answer: (a). Equal λ = h/mv means mp vp = mα vα. (vp)/(vα) = (mα)/(mp) = 4 So the answer is (a) 4: 1.

If the de Broglie wavelengths associated with a proton and an α… | JEE Main 2018 (15 Apr, Shift 2)

Q127JEE Main 2018 · 15 APR · SHIFT 2Easy

Matter Waves: de Broglie Wavelength

If the de Broglie wavelengths associated with a proton and an $\alpha$ -particle are equal, then the ratio of velocities of the proton and the $\alpha$ -particle will be:

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Answer: (a)

Equal $\lambda = \dfrac{h}{mv}$ means $m_p v_p = m_\alpha v_\alpha$ .
$\dfrac{v_p}{v_\alpha} = \dfrac{m_\alpha}{m_p} = 4$
So the answer is (a) $4 : 1$ .

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