For crystal diffraction experiments (discussed in Section 39.1), wavelengths on the order of 0.20 nm are often appropriate. Find the energy in electron volts for a particle with this wavelength if the particle is (a) a photon.

Verified step by step guidance

1. Use the formula for the energy of a photon, which is given by $E = hf$, where $h$ is Planck's constant and $f$ is the frequency of the photon.
2. To find the frequency $f$, use the relationship between wavelength $\lambda$, frequency $f$, and the speed of light $c$. The formula is $f = \frac{c}{\lambda}$, where $\lambda$ is the wavelength of the photon.
3. Substitute the value of $f$ from step 2 into the formula for energy $E = hf$.
4. Convert the energy from joules to electron volts (eV) using the conversion factor: 1 eV = 1.602 \times 10^{-19} joules.
5. Substitute the values of $h = 6.626 \times 10^{-34}$ J\cdot s (Planck's constant), $c = 3.00 \times 10^8$ m/s (speed of light), and $\lambda = 0.20$ nm (converted to meters as $0.20 \times 10^{-9}$ m) into the formulas and calculate the energy in electron volts.

Key Concepts

De Broglie Wavelength

The De Broglie wavelength is a fundamental concept in quantum mechanics that relates the wavelength of a particle to its momentum. It is given by the formula λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. This concept is crucial for understanding the wave-particle duality of matter and is applicable to photons and other particles.

Energy of a Photon

The energy of a photon is directly related to its wavelength and is calculated using the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. This relationship shows that shorter wavelengths correspond to higher energy photons, which is essential for analyzing the energy of particles in diffraction experiments.

Electron Volts (eV)

An electron volt (eV) is a unit of energy commonly used in the field of physics, particularly in particle physics and quantum mechanics. It is defined as the amount of kinetic energy gained by a single electron when it is accelerated through an electric potential difference of one volt. Understanding this unit is important for converting energy values from joules to eV, especially when dealing with photon energies.