Practice portal › Dual Nature of Matter and Radiation › Comparing de Broglie Wavelengths of Particles

A proton and an α-particle are passed through the same potential difference. If their initial velocity is zero, the ratio of their de Broglie wavelengths (λₚ:λ_α) after getting accelerated is ______.

Asked in RS Academy GUJCET booklet · Matter waves in other settings

• (1) 1:1
• (2) 1:2
• (3) 2:1
• (4) 2√2:1

Step-by-step solution

Why the other options are wrong

• (1) The same potential difference does not give the same wavelength. The α-particle has twice the charge, so it gains twice the kinetic energy, and it has four times the mass, so its momentum is larger.
• (2) No single slip gives 1:2. Sanity check: the proton is lighter and gains less energy, so its momentum is smaller and its wavelength longer; λₚ:λ_α must exceed 1.
• (3) This forgets the charge. Treating both as gaining the same kinetic energy gives √(m_α)/(mₚ) = √4 = 2, but the α-particle carries 2e and gains 2eV, not eV.

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