Many calculators use photocells as their energy source. Find...

Many calculators use photocells as their energy source. Find the maximum wavelength needed to remove an electron from silver $\left(\phi=7.59 \times 10^{-19} \mathrm{~J}\right)$. Is silver a good choice for a photocell that uses visible light? [The concept of the work function (\phi) is explained in Problem $7.69 .]$

Key Concepts

Photoelectric Effect

The photoelectric effect is a phenomenon in which electrons are emitted from a material when it absorbs light with sufficient energy. This effect demonstrates the particle nature of light, where incident photons transfer energy to electrons, overcoming the binding energy of the electrons in the material. It forms a key basis for understanding devices like photocells that convert light into electrical energy.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a material. It is a critical property in the photoelectric effect as it sets the threshold energy that an incident photon must have to free an electron from the material. A higher work function means that the material needs more energetic (shorter wavelength) photons for electron emission.

Threshold Wavelength

The threshold wavelength is the maximum wavelength (or minimum photon energy) needed to eject an electron from a material, calculated using the relation ? = hc/?, where ? is the work function, h is Planck's constant, and c is the speed of light. This concept is essential in determining whether a light source, such as visible light, has photons energetic enough to cause the photoelectric effect.

Visible Light

Visible light refers to the range of electromagnetic radiation that can be seen by the human eye, typically between wavelengths of about 400 nm and 700 nm. In the context of photocells, it is important to evaluate whether the material’s threshold wavelength falls within this range, ensuring that the light source used (if from the visible spectrum) can efficiently trigger the photoelectric effect.

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