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Light of wavelengths λ_A and λ_B is incident on two identical metal plates, and photoelectrons are emitted. If λ_A = 2λ_B, the maximum kinetic energies K_A and K_B of the photoelectrons are related as ______.

Asked in RS Academy GUJCET booklet · Speed and kinetic energy of the photoelectrons

Answer: (2) K_A < (K_B)/2

Step-by-step solution

Given: identical plates, so the same work function φ₀; λ_A = 2λ_B.

Idea: Einstein's equation K = (hc)/λ - φ₀.

For B: K_B = (hc)/(λ_B) - φ₀, so (hc)/(λ_B) = K_B + φ₀.

For A: K_A = (hc)/(2λ_B) - φ₀ = (K_B + φ₀)/2 - φ₀ = (K_B)/2 - (φ₀)/2

Since φ₀ > 0, K_A is less than (K_B)/2.

So K_A < (K_B)/2.

Why the other options are wrong

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