Question

What is meant by threshold wavelength?

Hint:

For the photoelectric effect, only photons with a wavelength shorter than the threshold wavelength can eject electrons from a material.

Answer 1

The threshold wavelength refers to the maximum wavelength of light or electromagnetic radiation that is capable of causing the emission of electrons from a material. This concept is most commonly used in the context of the photoelectric effect. When light strikes a material, the energy from the light can knock electrons out of the material, but only if the energy of the light is above a certain threshold. The energy of a photon is inversely proportional to its wavelength. Hence, the shorter the wavelength, the higher the energy of the photon. The threshold wavelength corresponds to the wavelength at which the photon’s energy is just enough to overcome the work function of the material (the energy required to remove an electron from the surface of the material). If the wavelength of the incoming light is longer than the threshold wavelength, the photon will not have enough energy to dislodge electrons from the material. Mathematically, the threshold wavelength \(\lambda_{th}\) is related to the work function \(\phi\) of the material by the equation: \[ \phi = \frac{hc}{\lambda_{th}} \] where: - \(\phi\) is the work function (in joules), - \(h\) is Planck’s constant (\(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}\)), - \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)), - \(\lambda_{th}\) is the threshold wavelength (in meters).