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Chapter 27: Problem 53

What is the maximum wavelength of a photon that can create an electron- positron pair?

Short Answer

Expert verified
Answer: The maximum wavelength of a photon that can create an electron-positron pair is approximately 1.214 nm.

Step by step solution

01

Identifying Relevant Equations

First, we need to keep in mind the energy-mass relationship for particles and the energy-frequency relationship for photons. The energy-mass relationship for particles is given by the equation: E_particle = m * c^2 The energy-frequency relationship for photons is given by the equation: E_photon = h * f Where E_particle is the energy of a particle, m is its mass, c is the speed of light, E_photon is the energy of a photon, h is the Planck's constant, and f is the frequency of the photon. Additionally, we can relate the frequency of a photon to its wavelength, λ, using the following equation: f = c / λ
02

Determine the Minimum Energy for Photon

An electron-positron pair can be created if the photon has enough energy to produce the pair. As the rest mass energy of both an electron and a positron is 0.511 MeV each, the minimum energy required for a photon to create an electron-positron pair is the sum of their energies: E_min = 2 * 0.511 MeV = 1.022 MeV
03

Convert Energy to Frequency

Now we need to convert this minimum energy to a frequency. We can use the energy-frequency relationship for photons to do this: 1.022 MeV = h * f_min f_min = 1.022 MeV / h
04

Convert Frequency to Wavelength

Finally, we need to convert this minimum frequency into a maximum wavelength using the equation relating frequency and wavelength: λ_max = c / f_min Plugging values of c and h: λ_max = (3e8 m/s) / (1.022 MeV / 6.63e-34 Js)
05

Calculate the Maximum Wavelength

Calculate the maximum wavelength by solving the equation in Step 4: λ_max = (3e8 m/s) * (6.63e-34 Js) / (1.022 MeV * 1.602e-13 J/MeV) λ_max ≈ 1.214e-12 m So, the maximum wavelength of a photon that can create an electron-positron pair is approximately 1.214 nm.

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