Question

A clean metal surface is irradiated with light of three different wavelengths λ1 , λ2 , and λ3 . The kinetic energies of the ejected electrons are as follows: λ1 : 7.2 × 10⁻²⁰ J; λ2 : approximately zero; λ3 : 5.8 × 10⁻¹⁹ J. Which light has the shortest wavelength and which has the longest wavelength? Determine the threshold frequency, νo, for this metal.

Answer 1

The light with kinetic energy of 5.8 \u00d7 10⁻¹⁹ J (\u03bb3) has the shortest wavelength, the light with kinetic energy of approximately zero (\u03bb2) has the longest, and the threshold frequency (\u03bd0) corresponds to the work function (\u03a6) divided by Planck's constant (h).

Step-by-step explanation:

To determine which light wavelength is shortest and which is longest, we use the fact that shorter wavelengths of light have higher energies because the energy of a photon is inversely proportional to its wavelength, according to the equation E = hf, where h is Planck's constant and f is the frequency. Given the kinetic energies, the light with kinetic energy of 5.8 \u00d7 10⁻¹⁹ J, \u03bb3, has the highest energy and therefore the shortest wavelength. In contrast, the light with kinetic energy of approximately zero, \u03bb2, has the longest wavelength, as it only imparts enough energy to just remove the electron without giving it additional kinetic energy. The threshold frequency, \u03bd0, can be found by applying Einstein's photoelectric equation to the case where the kinetic energy is approximately zero, which corresponds to the incident photon energy being equal to the work function (\u03a6). Thus, the threshold frequency is \u03bd0 = \u03a6/h.