Photons of energy E=4.000 keV undergo Compton scattering. What is the largest possible change in

Photons of energy E=4.000 keV undergo Compton scattering....

Photons of energy $E=4.000 \mathrm{keV}$ undergo Compton scattering. What is the largest possible change in photon energy, measured as a fraction of the incident photon's energy $\left(E-E^{\prime}\right) / E ?$

Key Concepts

Scattering Angle and Maximum Energy Transfer

The magnitude of the energy loss in Compton scattering is maximized when the photon scatters in the backward direction (? = 180°). This scenario results in the largest possible change in wavelength and hence energy, making it vital for understanding the limits of energy transfer from photons to electrons in the scattering process.

Compton Wavelength Shift

The Compton wavelength shift formula, ?? = (h/m_ec)(1 - cos?), quantifies the change in wavelength of a photon when it scatters off a free electron. This formula highlights the dependence of the wavelength change on the scattering angle (?) and is essential for calculating the energy change in the photon during the scattering event.

Photon Energy-Wavelength Relation

The energy of a photon is inversely proportional to its wavelength, expressed by the equation E = hc/?, where h is Planck's constant and c is the speed of light. This relationship is crucial in analyzing changes in a photon's energy by correlating them with shifts in its wavelength as it scatters.

Compton Scattering

Compton scattering describes the inelastic collision between a photon and a target particle, typically an electron. In this interaction, the photon loses some energy and changes direction while the electron gains kinetic energy. This phenomenon provided key evidence for the particle-like behavior of light and the quantization of electromagnetic radiation.

Transcript

00:01 In this exercise, we have photons with an energy of 4 kiloelectron volts, scattering of electrons, according to the compton scattering.

00:10 And we want to know what is the biggest difference in the photon in energy.

00:16 That is, the energy of the initial photon minus the energy of the final photon, the scattered photon, divide as a fraction of the incident photon's energy.

00:29 So this is what we're going to calculate.

00:31 Notice that if we want delta e equals to e minus e prime to be maximum, then e prime has to be minimum.

00:43 We have to calculate what is the minimum energy of the scattered photon.

00:48 Now remember that the energy of a photon is given by ahc over lambda.

00:54 Here i'm going to use lambda prime for the wavelength of the scattered photon.

01:00 So that if we want the smallest energy e -prime, we're looking for the biggest wavelength lambda prime.

01:11 Now, according to compton's formula, we have that the wavelength of the scattered photon equals the wavelength of the incident photon, plus h over mcm is the mass of the electron, 1 minus cosine theta.

01:29 Notice that the angle for which the for which lambda prime is going to be the largest is 100 theta equals 180 degrees.

01:43 Because when that's true, when theta equals 108 degrees, the cosine of theta is minimum, which is minus 1.

01:52 And we're going to have lambda prime equals lambda plus 2h over mc.

02:01 The biggest wavelength possible...

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