Light of wavelength $λ_{A}$ and $λ_{B}$ falls on two identical metal plates A and B, respectively. The
maximum kinetic energy of photoelectrons is K_A and K_B respectively, then which one of the following
relations 'is true? ( $λ_{A}$ = 2 $λ_{B}$ )

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$K_{A} < \frac{K_{B}}{2}$

2K_A = K_B

K_A = 2K_B

K_A > 2K_B

answer is A.

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Detailed Solution

According to Einstein's photoelectric equation,

$K_{A} = \frac{h c}{λ_{A}} - ϕ \Rightarrow K_{A} + ϕ = \frac{h c}{λ_{A}}$

$K_{B} = \frac{h c}{λ_{B}} - ϕ = \frac{h c}{(λ_{A} / 2)} - ϕ$

or $K_{B} = \frac{2 h c}{λ_{A}} - ϕ = 2 (K_{A} + ϕ) - ϕ = 2 K_{A} + ϕ \Rightarrow K_{A} < \frac{K_{B}}{2}$

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