Question

Ultraviolet light is more likely to induce a current in a metal than visible light. This is because photons of ultraviolet light: (A) have a longer wavelength. (B) have a higher velocity. (C) are not visible. (D) have a higher energy.

Short answer

The correct answer is (D) have a higher energy.

Step-by-step solution

- Understand the Problem

To solve this, first understand why ultraviolet light is more effective at inducing a current in a metal compared to visible light. This requires knowledge about the properties of light.

- Analyze the Properties of Light

Ultraviolet light and visible light are both forms of electromagnetic radiation, but they have different wavelengths and energies. Ultraviolet light has shorter wavelengths and higher energy compared to visible light.

- Determine the Relationship Between Photon Energy and Metal

The probability of inducing a current in a metal is related to the energy of the photons. According to the photoelectric effect, when photons strike a metal surface, they can eject electrons if their energy exceeds the metal's work function.

- Identify the Correct Statement

Among the given options, the correct reason why ultraviolet light is more likely to induce a current is because ultraviolet photons have higher energy compared to visible light photons.

- Choose the Correct Answer

Based on the analysis, the correct answer is (D) have a higher energy.

Key concepts

Photon Energy

Photon energy is a crucial concept when understanding the behavior of light in different scenarios.
A photon is a particle of light and carries energy. The energy of a photon is directly related to its frequency and inversely related to its wavelength. This relationship is expressed in the equation:
E = h u where E is the energy of the photon, h is Planck's constant, and u is the frequency of the light.
This means that higher frequency light, like ultraviolet (UV) light, has higher energy photons compared to lower frequency, visible light. When these high-energy photons hit a metal, they are more likely to eject electrons from the metal. This phenomenon is central to the photoelectric effect, explaining why UV light is more efficient in inducing current in metals.

Ultraviolet Light

Ultraviolet light (UV light) is a type of electromagnetic radiation with wavelengths shorter than visible light but longer than X-rays.
We categorize UV light into three main types based on wavelength:

• UVA (longest wavelength)
  
• UVB
  
• UVC (shortest wavelength)
  

UV light is not visible to the human eye and possesses higher photon energy compared to visible light. This higher energy allows UV photons to eject electrons more effectively from metal surfaces, making UV light particularly significant in studies of the photoelectric effect.

Electromagnetic Radiation

Electromagnetic radiation encompasses a wide range of wavelengths and frequencies, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
Each type of radiation in the spectrum differs in wavelength and frequency:

• Radio waves have the longest wavelength and lowest frequency.
  
• Gamma rays have the shortest wavelength and highest frequency.
  
• Visible light falls in between, with UV light having shorter wavelengths and higher frequencies than visible light.
  

All forms of electromagnetic radiation travel at the speed of light in a vacuum. The energy of these waves is carried by photons, and the energy of individual photons increases with frequency. Understanding this spectrum helps explain why UV light, part of the high-energy end, is effective in inducing the photoelectric effect.

Wavelength

Wavelength is the distance between successive crests of a wave. In the context of light and electromagnetic radiation, wavelength determines the type and energy of the radiation.
Ultraviolet light has a shorter wavelength compared to visible light. The shorter the wavelength, the higher the frequency, and thus, the higher the energy of the photons.
This relationship is important because it means that UV light photons have significantly higher energy than visible light photons, which is essential for triggering the photoelectric effect.
In summary, understanding how wavelength affects the energy of light can help explain why certain types of light are more effective in various applications, such as in the generation of electric currents in metals.