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

An electron and a proton are moving in the same direction with the same kinetic energy. The ratio of the de Broglie wavelength of the electron to that of the proton is ______.

Asked in GUJCET 2011 · Same or changed energy

• (1) (mₑ)/(mₚ)
• (2) (mₚ)/(mₑ)
• (3) √(mₚ)/(mₑ)
• (4) mₚ· mₑ

Step-by-step solution

Why the other options are wrong

• (1) (mₑ)/(mₚ) would make the electron's wavelength the shorter one, and it drops the square root; at equal kinetic energy λ ∝ 1/(√m).
• (2) (mₚ)/(mₑ) is the ratio for equal speeds, where λ = h/(mv). At equal kinetic energy the momentum is √2mK, which brings in a square root.
• (4) A product of two masses has the unit kg², so it cannot be a ratio of two wavelengths, which has no unit.

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