The work function of metal A is less than that of metal B....

The work function of metal A is less than that of metal B. (a) The threshold wavelength for metal A is (1) shorter than, (2) the same as, (3) longer than that of metal B. Why? (b) If the threshold wavelength for metal B is $620 \mathrm{nm}$ and the work function of metal $\mathrm{A}$ is twice that of metal B, what is the threshold wavelength for metal A?

The work function of metal A is less than that of metal B. (a) The threshold wavelength for metal A is
(1) shorter than, (2) the same as, (3) longer than that of metal B. Why? (b) If the threshold wavelength for metal B is $620 \mathrm{nm}$ and the work function of metal $\mathrm{A}$ is twice that of metal B, what is the threshold wavelength for metal A?

Key Concepts

Energy-Wavelength Relationship

The energy of photons is inversely related to their wavelength according to the equation E = hc/?, where h is Planck’s constant and c is the speed of light. This relationship explains why, for metals with different work functions, the threshold wavelength shifts such that a metal with a lower work function has a longer threshold wavelength compared to one with a higher work function.

Photoelectric Effect

The photoelectric effect is the phenomenon where electrons are emitted from a metal surface upon exposure to light of adequate energy. This effect demonstrates the quantization of light and is explained by the requirement that the energy of an incident photon must be equal to or greater than the work function of the material for electrons to be ejected.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a metal. It is a material property expressed in energy units (typically electron volts) and is a key factor in determining how easily electrons can be ejected from a metal when light shines on it.

Threshold Wavelength

The threshold wavelength represents the longest wavelength (or equivalently, the lowest photon energy) that can cause photoemission from a metal surface. It is intrinsically linked to the work function by the relation ? = hc/?, meaning that a lower work function results in a longer threshold wavelength.

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