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

A proton and an electron have the same de Broglie wavelength. If Kₚ and Kₑ be the kinetic energies of proton and electron respectively, then choose the correct relation

Asked in JEE Main 8th April 2nd Shift 2024 · Equal wavelengths and equal speeds

• (1) Kₚ=Kₑ
• (2) Kₚ>Kₑ
• (3) Kₚ=Kₑ²
• (4) Kₚ<Kₑ

Step-by-step solution

Why the other options are wrong

• (1) comes from assuming equal wavelengths mean equal energies, which would need equal masses too
• (2) comes from expecting the heavier particle to carry more energy at the same momentum
• (3) comes from has no dimensional sense; energies cannot equal the square of an energy

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