Cerenkov Luminescence Imaging: Physics Principles and Potential Applications in Biomedical Sciences

Problem 9 ¼. The end point kinetic energy (see Fig. 17.8) for beta decay of 131I is 606 keV, and tissue has an index of refraction of 1.4. Do any of the emitted electrons have a speed faster than the speed of light in the tissue? To determine this speed, use Eq. 14.1. Because the electrons move near the speed of light, to determine their speed as a function of their kinetic energy use a result from special relativity, Eq. 17.1.

Problem 9 ½. The drawing below shows a particle moving to the right faster than the speed of light in the medium. The position of the particle at several instants is indicated by the purple dots. The location of light emitted by the particle at each position is shown by the black circles. The light adds to form a conical wave front, shown by the green lines.

(a) Use the red right triangle to calculate the angle θ as a function of the particle speed, v, and the index of refraction, n.

(b) Compute the value of θ for the fastest electrons emitted by beta decay of 131I in tissue.

Problem 9 ¾. The number of photons dN emitted with a wavelength between λ and λ + is approximately dN = Cdλ/λ2, where C is a constant.

(a) Sketch a plot of dN/ versus λ. Don’t worry about the scale of the axes (in other words, don’t worry about the value of C); just make the plot qualitatively correct.

(b) Use methods similar to those introduced in Section 14.8 to determine the number of photons emitted with an energy between E and E + dE. Don’t worry about constant factors, just determine how dN/dE varies with E.

(c) Sketch a plot of dN/dE versus E. Again, just make the plot qualitatively correct.

How does Cerenkov radiation work?

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