Suppose light of a longer wavelength has shone on the potassium. Would photoelectrons emission take place exaplain?

You need to provide more details. This seems to just part of the problem.

Yes, if light of a longer wavelength shines on potassium, photoelectron emission can still take place. To understand why, let's break it down step by step:

1. Photoelectric Effect: The photoelectric effect refers to the emission of electrons (called photoelectrons) from a material when it is exposed to light. In this process, the energy of the incident photons determines whether electrons can be released from the material.

2. Longer Wavelength: Wavelength is a property of light that determines its color or frequency. Longer wavelengths correspond to lower frequencies and lower energies, while shorter wavelengths correspond to higher frequencies and higher energies.

3. Energy of Photons: The energy of a photon is directly proportional to its frequency (and inversely proportional to its wavelength). So, longer wavelengths correspond to lower energy photons, and vice versa.

4. Energy Threshold: For an electron to be emitted from a material, it must overcome a certain energy threshold, often referred to as the "work function" of the material. The work function is the minimum amount of energy required to remove an electron from the material's surface.

5. Absorption of Photons: When light interacts with a material, its photons may be absorbed, reflected, or transmitted through the material. If the incident photon's energy is greater than or equal to the work function of the material, photoelectron emission can occur.

6. Photoelectron Emission: When a photon is absorbed by an atom or a solid material, it transfers its energy to one of the electrons in that material. If the photon's energy is sufficient to overcome the work function, the electron can be released as a photoelectron.

In the case of potassium, it has a relatively low work function, which means that even photons with lower energies (such as those associated with longer wavelengths) can provide enough energy to release photoelectrons. Therefore, if light of a longer wavelength shines on potassium, photoelectron emission can still occur, provided the energy of the photons is above the work function of potassium.