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

If an alpha particle and a deuteron move with velocities v and 2v respectively, the ratio of their de Broglie wavelengths will be ______.

Asked in GUJCET 2015 · Matter waves in other settings

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

Step-by-step solution

Why the other options are wrong

• (1) This uses the speeds alone, λ ∝ 1/v, giving (λ_α)/(λ_d) = (2v)/v = 2. It forgets that the α-particle is also twice as heavy as the deuteron.
• (2) This uses λ ∝ 1/(√m), which holds only when the kinetic energies are equal: √(m_d)/(m_α) = √2/4 = 1/(√2). Here the speeds are given, and the momenta turn out equal.
• (4) This uses λ ∝ 1/(√K) and drops the mass from λ = h/(√2mK): with K_α = 2uv² and K_d = 4uv², √(K_d)/(K_α) = √2.

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