Problem 20 - Chemistry The Molecular Science

Question

Light of very long wavelength strikes a photosensitive metallic surface and no electrons are ejected. Explain why increasing the intensity of this light on the metal still will not cause the photoelectric effect.

Step-by-Step Solution

Answer

Increased intensity does not change the low energy of long-wavelength light, hence no electrons are ejected.

Step 1: Understand the Photoelectric Effect

The photoelectric effect occurs when light shining on a metallic surface causes the ejection of electrons. According to the theory, the light must have a minimum threshold frequency (related to energy) to overcome the work function of the metal and release electrons.

Step 2: Wavelength and Energy Relationship

The energy of a photon is inversely related to its wavelength: \( E = \frac{hc}{\lambda} \), where \( E \) is energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength. Very long wavelengths correspond to low-energy photons.

Step 3: Intensity vs. Frequency

Increasing the intensity of the light increases the number of photons but does not increase the energy per photon. Intensity refers to the total power per unit area but does not affect the energy carried by each individual photon.

Step 4: Energy Requirement for Electron Ejection

For electrons to be ejected from the metal surface, the energy of individual photons (which is determined by their frequency) must be greater than or equal to the metal's work function. Intensity does not change this energy requirement since it only affects photon quantity, not energy per photon.

Step 5: Conclusion of Light Intensity

Increasing the light intensity of "very long wavelength light" results in more low-energy photons but none having sufficient energy to exceed the metal's work function, hence no electrons are ejected despite the increased intensity.

Key Concepts

Wavelength and Energy Relationship

In the context of the photoelectric effect, the relationship between wavelength and energy is crucial to understanding why certain light cannot eject electrons from a metal surface. The energy of a photon is inversely proportional to its wavelength. This means that as the wavelength increases, the energy associated with each photon decreases. The formula representing this relationship is \( E = \frac{hc}{\lambda} \), where \( E \) is the photon energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength of light.

• Long wavelength light implies low-energy photons.
• Shorter wavelengths yield higher photon energies.
• This relationship dictates the capability of light in terms of providing enough energy to eject electrons from a material.

In practical terms, if the light has a very long wavelength, its energy might not be sufficient to overcome the work function of a metal, meaning it cannot cause electron ejection regardless of its intensity.

Intensity vs. Frequency

Understanding the distinction between intensity and frequency is key to grasping the mechanics behind the photoelectric effect. Intensity refers to the number of photons striking an area, but it doesn't impact the energy of each photon. On the other hand, frequency is directly related to the energy of the photons themselves.

• Intensity describes the photon count — higher intensity means more photons but not more energy per photon.
• Frequency directly impacts photon energy, with higher frequencies meaning higher energies.
• For electron ejection, the focus must be on frequency, not intensity.

Therefore, even if the light's intensity is increased, without a suitable frequency (which determines photon energy), electrons will not be ejected because the photons do not possess the necessary energy to overcome the metal's work function.

Work Function of Metals

The work function of a metal is the minimum energy required to eject an electron from the surface of that metal. This property varies between different metals and plays a critical role in the photoelectric effect. In order for electrons to be emitted, the energy of incoming photons must be greater than or equal to this work function.

• The work function is a fixed property for each type of metal.
• If photon energy, dictated by frequency, is below this threshold, no electron emission occurs.
• Even high-intensity light producing no photon energy exceeding the threshold will not help in ejecting electrons.

Thus, regardless of how many low-energy photons are striking the metal due to increased intensity, if they do not possess the required energy equivalent to the work function, the photoelectric effect will not occur, and no electrons will be liberated from the metal surface.