It is observed that light of 430 nm just begins to emit photoelectrons. What is the classical prediction if the wavelength of the incident light is changed to 440 nm?

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We start by clarifying the setup: at 430 nm light, photoelectrons just begin to be emitted, which implies we are at the threshold energy where photons have just enough energy to overcome the work function of the surface. Now, we examine what happens if the wavelength is changed to 440 nm.

Option a: photocurrent increases immediately. This would suggest that moving to a longer wavelength somehow boosts emission, which contradicts the concept of a threshold at 430 nm. If anything, moving farther from threshold should not increase emission in the classical picture, so this is unlikely.

Option b: photocurrent increases gradually. This implies a rising emission due to longer wavelength, which again clashes with the threshold idea. In classical terms, emission is not driven by a gradual change with wavelength near threshold, so this reasoning is misplaced.

Option c: photocurrent decreases immediately. An immediate drop would require a sudden dependence of emission on wavelength right at 430–440 nm, but the key point is that at 430 nm we are at the threshold; the classical framework does not predict a per-photon energy constraint that causes an abrupt drop as you move to 440 nm.

Option d: photocurrent decreases gradually. This suggests a smooth, wavelength-dependent change in current, again implying a photon-energy-based mechanism. Classical theory does not tie current to a per-photon energy constraint in the same way as the quantum description, so this gradual decrease is not the orthodox classical prediction.

Option e: no change in the photo current. Under classical (non-quantized) thinking, the emission current is primarily tied to the light intensity, not to the photon energy relative to a threshold. Since we are keeping the light intensity the same and only increasing the wavelength slightly (still near the same energy scale in classical terms), the predicted current would remain essentially unchanged.

Option f: Cannot be determined. Given the stated observation at 430 nm and the classical perspective described above, there is enough information to state a prediction: the classical view would not attribute a threshold-driven change to this small shift in wavelength, so it can be determined that the current does not change with the wavelength shift in the classical picture.

In summary, the classical viewpoint treats photoelectric emission as governed mainly by light intensity rather than a strict photon-energy threshold. Therefore, changing the wavelength from 430 nm to 440 nm, while keeping other conditions constant, would not produce a change in the photocurrent according to classical reasoning. The option that captures this is the one indicating no change in the photo current. The remaining options push conclusions that align more with a photon-energy threshold effect, which is not the classical prediction here.

MUF0122 Physics Unit 2 - Semester 2, 2025 13.7 Photoelectric effect

It is observed that light of 430 nm just begins to emit photoelectrons. What is the classical prediction if the wavelength of the incident light is changed to 440 nm?

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