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

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Question restatement: The scenario states that light of 430 nm just begins to emit photoelectrons. If the incident wavelength is changed to 440 nm, what does quantum theory predict for the photocurrent?

Option a: photocurrent increases immediately. This is unlikely because increasing the wavelength (reducing photon energy) cannot increase the emission rate once you are at or below the threshold energy. Since 430 nm is the threshold where emission just starts, moving to 440 nm provides even less energy, not more, so the current would not rise.

Option b: photocurrent increases gradually. Similar to option a, an increase in wavelength reduces photon energy, so there is no mechanism here to cause a gradual rise in current. The emission rate should not increase as photons become less energetic.

Option c: photocurrent decreases immediately. This aligns with the photoelectric effect: if the photon energy falls below the work function (which occurs when wavelength exceeds the threshold 430 nm), no electrons are emitted, so the photocurrent drops to zero. The transition from near-threshold emission at 430 nm to 440 nm would produce an immediate decrease to no current.

Option d: photocurrent decreases gradually. A gradual decrease would imply a continuous partial emission as energy falls below threshold, which contradicts the quantum threshold behavior: once the photon energy is below work function, emission ceases, not gradually diminishes.

Option e: no change in the photo current. This contradicts the fundamental threshold behavior: moving to a wavelength with insufficient energy eliminates emission altogether, so the current cannot stay the same.

Option f: Cannot be determined. The scenario provides clear threshold information: 430 nm is the threshold; at 440 nm the energy is insufficient, so emission should cease. Therefore, it is determinable.

In summary, understanding the photoelectric effect shows that photon energy must exceed the work function to eject electrons. Since 440 nm photons have lower energy than needed, no photoelectrons are emitted and the photocurrent drops to zero, which corresponds to option c. The other options misinterpret how emission depends on photon energy relative to the threshold.

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 quantum prediction if the wavelength of the incident light is changed to 440 nm?

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