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The wavelength λₑ of an electron and λₚ of a photon of the same energy E are related by:

Asked in NEET 2013 · Matter wave against photon

• (1) λₚ∝√λₑ
• (2) λₚ∝1/(√λₑ)
• (3) λₚ∝λₑ²
• (4) λₚ∝λₑ

Step-by-step solution

Why the other options are wrong

• (1) comes from takes a square root where the algebra takes a square: the electron's energy goes as 1/λₑ², so substituting it squares the relation rather than rooting it
• (2) comes from carrying λₚ=(hc)/E straight through as an inverse relation without substituting E=(h²)/(2mₑλₑ²) for the electron
• (4) comes from assumes the two wavelengths track each other directly, which would hold only if the photon and the electron shared the same momentum rather than the same energy

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