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An electron with speed v and a photon with speed c have the same de Broglie wavelength. If the kinetic energy and momentum of electron are Eₑ and pₑ and that of photon are Eₚₕ and pₚₕ respectively. Which of the following is correct?

Asked in JEE Main 26th June 1st Shift 2022 · Matter wave against photon

• (1) (Eₑ)/(Eₚₕ)=(2c)/v
• (2) (Eₑ)/(Eₚₕ)=v/(2c)
• (3) (pₑ)/(pₚₕ)=(2c)/v
• (4) (pₑ)/(pₚₕ)=v/(2c)

Step-by-step solution

Why the other options are wrong

• (1) comes from inverts the energy ratio, making the slow electron the more energetic
• (3) comes from gives the momenta a ratio, when equal wavelengths force them to be equal
• (4) comes from the same error with the ratio inverted

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