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A light source emitting only 400 nm wavelength (selected by an interference filter) shines on a metal surface and ejects electrons. The filter is then swapped for one that passes only 300 nm, and the lamp intensity falling on the metal is kept identical to before. Which statement correctly describes the situation with 300 nm light compared to 400 nm light?

1. More electrons are emitted per unit time.
2. The emitted electrons have greater kinetic energy.
3. Both: more electrons are emitted per unit time AND they are more energetic.
4. Neither statement is true.

Correct answer: The emitted electrons have greater kinetic energy.

Solution

At the same intensity, switching from 400 nm to 300 nm means each photon carries more energy (E = hc/lambda is larger), so there are fewer photons per second hitting the surface, meaning fewer photoelectrons are emitted. However, each emitted electron gains more kinetic energy (KE = hf - phi), so the electrons are more energetic.

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