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A photosensitive metallic surface has work function φ₀. If photons of energy 3φ₀ fall on this surface, the electrons come out with a maximum velocity of 6×10⁶ m s⁻¹. When the photon energy is increased to 9φ₀, the maximum velocity of the photoelectrons will be ______.

Asked in GUJCET 2011 · Speed and kinetic energy of the photoelectrons

• (1) 12×10⁶ m s⁻¹
• (2) 6×10⁶ m s⁻¹
• (3) 3×10⁶ m s⁻¹
• (4) 24×10⁶ m s⁻¹

Step-by-step solution

Why the other options are wrong

• (2) The maximum speed is not fixed by the metal alone. A larger photon energy leaves more kinetic energy after paying φ₀, so the speed must rise.
• (3) Comes from putting the ratio upside down: 6×10⁶×√(2φ₀)/(8φ₀) = 3×10⁶ m s⁻¹. The larger kinetic energy must give the larger speed.
• (4) Comes from forgetting the square root. The kinetic energy grows four times, from 2φ₀ to 8φ₀, but the speed grows only √4 = 2 times, not 4 times.

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