A photosensitive metallic surface has work function φ. If photon of energy 3φ falls on the surface, the electron comes out with a maximum velocity of 6 × 10⁶ m/s. When the photon energy is increased to 9φ, then maximum velocity of photoelectrons will be (a) 12 × 10⁶ m/s (b) 6 × 10⁶ m/s (c) 3 × 10⁶ m/s (d) 24 × 10⁶ m/s

Answer: (a). 1/2mv² = E - φ K₁ = 3φ - φ = 2φ, K₂ = 9φ - φ = 8φ v₂ = v₁√(8/2) = 2×6×10⁶ = 12×10⁶ m/s So the answer is (a) 12×10⁶ m/s.

A photosensitive metallic surface has work function φ. If photon of… | MHT CET 2024 (4 May, Shift 2)

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Photoelectric Effect: Einstein's Equation

A photosensitive metallic surface has work function $\phi$ . If photon of energy $3\phi$ falls on the surface, the electron comes out with a maximum velocity of $6 \times 10^{6}\text{ m/s}$ . When the photon energy is increased to $9\phi$ , then maximum velocity of photoelectrons will be

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Answer: (a)

$\frac{1}{2}mv^2 = E - \phi$
$K_1 = 3\phi - \phi = 2\phi$ , $K_2 = 9\phi - \phi = 8\phi$
$v_2 = v_1\sqrt{\frac{8}{2}} = 2\times6\times10^{6} = 12\times10^{6}\text{ m/s}$
So the answer is (a) $12\times10^{6}$ m/s.

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