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If wavelength of photon and electron is same then ratio of total energy of electron to total energy of photon would be:

1. \( \frac{\text { Velocity of electron }}{\text { Light's speed }} \)
2. \( \frac{\text { Light's speed }}{\text { Electon's speed }} \)
3. \( \frac{\text { Light's speed }}{\text { Velocity of electron }} \)
4. \( \frac{\text { Electron's speed }}{\text { Light's speed }} \)

Correct answer: \( \frac{\text { Velocity of electron }}{\text { Light's speed }} \)

Solution

For a photon, total energy is E = hc/λ. For an electron with the same wavelength, its momentum is p = h/λ, so its total energy in this context is proportional to pc = hc/λ times the speed ratio, giving E_e/E_γ = v/c. Hence the ratio is electron speed divided by light speed.

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