Question

A surface ejects electrons when hit by violet light but not when hit by yellow light. Will electrons be ejected if the surface is hit by red light? (1) Yes (2) No (3) Yes, if the red beam is quite intense (4) Yes, if the red beam continues to fall upon the surface for some time

Short answer

No

Step-by-step solution

- Understand the Photoelectric Effect

The photoelectric effect explains that electrons are ejected from a material when it is exposed to light of sufficient energy. The energy of the light must be higher than the work function of the material for electrons to be emitted.

- Compare Energies of Different Light Colors

Light energy depends on its wavelength or frequency. Violet light has a shorter wavelength and higher energy than yellow and red light. Yellow light has more energy than red light but less than violet light.

- Analysis for Violet and Yellow Light

Given that violet light causes electron ejection and yellow light does not, it can be concluded that violet light has enough energy to overcome the work function of the material, while yellow light does not.

- Consider the Energy of Red Light

Red light has an even longer wavelength and, therefore, less energy than both violet and yellow light. Since yellow light does not have enough energy to eject electrons, neither will red light.

- Addressing the Intensity and Duration

The intensity (brightness) or duration (how long the light shines) is irrelevant because the photoelectric effect depends on the energy of individual photons, not the quantity or duration.

Key concepts

Electron Ejection

The process when electrons are released from a material after absorbing energy from light is known as electron ejection. This occurs through the photoelectric effect. During this process, light hits the material's surface and provides energy to the electrons. If the energy is enough to overcome the material's work function, the electrons will be ejected from the surface. It's crucial to understand that not all light will cause electron ejection - the light must have enough energy to release the electrons.

Light Energy

The energy of light plays a fundamental role in the photoelectric effect. Light is composed of particles called photons, each carrying a specific amount of energy. The energy of these photons is determined by the light's wavelength and frequency. Shorter wavelengths—like those of violet light—carry more energy compared to longer wavelengths like those of red light. Thus, to eject electrons, the light must have photons with sufficient energy. This energy is quantified using the equation: \[E = h \times f\] where \(E\) is the energy of the photon, \(h\) is Planck's constant, and \(f\) is the frequency of the light.

Work Function

The work function is the minimum amount of energy needed to eject an electron from a material. Different materials have different work functions, meaning the energy required to release an electron varies based on the material. For the photoelectric effect to occur, the energy of the incoming photons must be greater than or equal to the work function. If the energy is lower, electrons will not be ejected regardless of the light's intensity or duration. This is why red light, which has less energy, cannot eject electrons from the surface if violet light is required.

Wavelength and Frequency

Wavelength and frequency of light are two key properties that determine its energy. Wavelength is the distance between two peaks of a wave, while frequency is the number of waves that pass a point in one second. They are inversely related—meaning when the wavelength increases, the frequency decreases and vice versa. The equation \[c = \lambda \times f\] relates them, where \(c\) is the speed of light, \(\lambda\) (lambda) is the wavelength, and \(f\) is the frequency. Thus, light with shorter wavelengths (like violet light) has higher frequencies and therefore higher energy. Conversely, light with longer wavelengths (like red light) has lower frequencies and less energy. This helps explain why red light is insufficient to cause electron ejection in some materials while violet light can.