Determining the Wavelength of a Photon with 1.1 eV Energy

Understanding the relationship between photon energy and its wavelength is a fundamental concept in quantum physics. Specifically, this relationship is crucial for various applications in science, technology, and engineering. In this article, we will explore how to calculate the wavelength of a photon that has an energy of 1.1 electron volts (eV).

Introduction to the Problem

The problem at hand involves finding the wavelength (lambda) of a photon with an energy of 1.1 eV. To solve this, we can use the fundamental equation that relates the energy of a photon to its wavelength. This equation is derived from both Planck's law and the relationship between the speed of light and frequency of the photon:

Equations and Calculations

The relationship between the energy (E) of a photon and its wavelength (lambda) is given by the equation:

[ E frac{hc}{lambda} ]

where:

(h) is Planck's constant ((6.626 times 10^{-34}) J·s) (c) is the speed of light in vacuum ((3 times 10^8) m/s) (lambda) is the wavelength of the photon in meters (E) is the energy of the photon in joules (J)

Note that when working with energies in electron volts (eV), we can simplify the calculations by using the conversion factor:

[ 1 text{ eV} 1.602 times 10^{-19} text{ J} ]

To convert from eV to nanometers (nm), we can use the simplified version of the equation:

[ lambda frac{1242 text{ nm} cdot text{eV}}{E_{text{eV}}} ]

Step-by-Step Calculation

Let's calculate the wavelength step-by-step using the given energy of 1.1 eV:

Convert the energy from eV to joules:

[ E 1.1 text{ eV} 1.1 times 1.602 times 10^{-19} text{ J} 1.7622 times 10^{-19} text{ J} ]

Using the full equation with Planck's constant and the speed of light:

[ lambda frac{hc}{E} frac{6.626 times 10^{-34} text{ J·s} times 3 times 10^8 text{ m/s}}{1.7622 times 10^{-19} text{ J}} approx 1.129 times 10^{-6} text{ m} 1129.099 text{ nm} ]

Alternative Method: Using Simplified Equation

For easier calculation, we can use the simplified form of the equation:

[ lambda frac{1242 text{ nm} cdot text{eV}}{1.1 text{ eV}} 1129.099 text{ nm} ]

This method confirms our previous result.

Comparison with Visible Spectrum

It is important to note the wavelength we calculated (1129.099 nm) falls in the near-infrared (NIR) region, which is beyond the visible spectrum (400 nm to 700 nm). This is typical for photons with energies above 1 eV, which correspond to the infrared region.

Conclusion

The wavelength of a photon with 1.1 eV energy is approximately 1129.099 nm, which falls in the near-infrared region. This calculation is fundamental in understanding the behavior of photons and is widely applicable in various scientific and technological fields, including spectroscopy and optical design.

Related Topics

For a deeper understanding of this topic, you may also want to explore the following related areas:

Quantum Physics Spectroscopy Optical Properties of Materials