When a positron and an electron collide and annihilate each other, two photons of equal energy are produced. What is the wavelength of these photons?

Verified step by step guidance

1. Understand that when a positron and an electron annihilate, their mass is converted into energy in the form of photons.
2. Use the equation for energy-mass equivalence, $E = mc^2$, to calculate the total energy released, where $m$ is the mass of the electron (or positron) and $c$ is the speed of light.
3. Since two photons are produced, divide the total energy by 2 to find the energy of each photon.
4. Use the equation for the energy of a photon, $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant and $\lambda$ is the wavelength, to solve for the wavelength of each photon.
5. Rearrange the equation to solve for $\lambda$: $\lambda = \frac{hc}{E}$, and substitute the known values to find the wavelength.

Key Concepts

Annihilation Reaction

Annihilation occurs when a particle and its antiparticle collide, resulting in their conversion into energy. In this case, when a positron (the antiparticle of the electron) meets an electron, they annihilate each other, producing energy in the form of photons. This process exemplifies the principle of mass-energy equivalence, as described by Einstein's equation E=mc².

Photon Energy and Wavelength Relationship

The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. This relationship indicates that higher energy photons have shorter wavelengths. Understanding this concept is crucial for calculating the wavelength of photons produced in the annihilation process.

Conservation of Energy

In any physical process, the total energy before and after must remain constant, a principle known as the conservation of energy. In the case of electron-positron annihilation, the total rest mass energy of the electron and positron is converted into the energy of the two photons. This principle allows us to determine the energy of the photons produced, which can then be used to find their wavelength.