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MCAT

Unit 3: Lesson 1

Chemical and physical sciences practice passage questions

Imaging tissue structures using muon tomography

Problem

Muons are elementary, charged particles that undergo the same interactions as electrons, but which have much greater masses. For this reason, muons could be used as an alternative to electrons in transmission microscopy, in which the pattern formed by scattered, charged particles after passing through a sample may be used to infer the structure of biological tissues. Such methods are useful for probing structural details of biological materials that are smaller than the optical diffraction limit, which determines the smallest feature sizes that can be observed using a traditional, light-based microscope.
A simple muon detector (Figure 1) consists of an array of diodes. Each diode emits an electric signal when a muon passes through it, and so the specific diode in the array that emits a signal after a muon strike indicates the two-dimensional location of the strike. A beam of muons with known energy passes through the sample, and at each beam location, the location on the detector plate at which muons arrive after passing through the sample is recorded. Locations at which the beam was most strongly deflected indicate the presence of internal structures, resulting in a two-dimensional image of the tissue. The total deflection of the incident beam by the sample is, at most, a few degrees for the densest parts of the sample.
This technique has recently been generalized to provide three-dimensional information about samples in a method known as muon tomography. In order to gain information about the three-dimensional scattering field with which the muon interacts before it reaches the detector, the direction that each muon is traveling after it exits the tissue sample must be known. This method requires at least two detector arrays, since the velocity vector of the muon can be calculated from the 2D location on each detector array where the muon struck, the distance between the two arrays, and the time between the two detection events. Assume that the muons are heavy enough to be treated as point masses subject to classical electromagnetism and Newton’s laws. Additionally, assume that the detectors themselves barely affect the muons’ trajectories.
Figure 1: The elements of a muon measurement assembly. Muons exit the source and are deflected as they pass through the sample. The deflected muons pass through one of the diodes in the diode array, which indicates their position in the plane of the array.
Which of the following best describes the cause of the small-angle deflections of the incident muon beam?
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