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An electron and a photon have the same energy E. If their wavelengths are denoted by λₑ and λₚ respectively, which relation between them is correct?

1. λₚ is directly proportional to λₑ
2. λₚ is proportional to the square root of λₑ
3. λₚ is proportional to the inverse square root of λₑ
4. λₚ is proportional to λₑ squared

Correct answer: λₚ is proportional to λₑ squared

Solution

The correct option indicates that the wavelength of the photon is proportional to the square of the wavelength of the electron, which arises from the different relationships between energy and wavelength for particles with mass (like electrons) and massless particles (like photons). This reflects the fundamental differences in how their energies relate to their wavelengths.

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