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The de Broglie wavelengths of a proton and an α-particle are the same. Which physical quantity should then be the same for both?

Asked in RS Academy GUJCET booklet · Equal wavelengths and equal speeds

• (1) velocity
• (2) energy
• (3) frequency
• (4) momentum

Step-by-step solution

Why the other options are wrong

• (1) Equal momentum with unequal masses means unequal speeds: the α-particle is about four times heavier, so the proton moves about four times faster.
• (2) Kinetic energy is (p²)/(2m). With the same p, the lighter proton has about four times the kinetic energy of the α-particle.
• (3) The relation λ = h/p fixes the momentum, not a frequency. The two particles have different speeds and energies, so equal wavelengths do not give them a common frequency.

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