A mass spectrometer similar to the one in Figure P 24.67 is designed to analyze biological sampl

step 1 In the given problem, there is a mass spectrometer. Here, the charged particles enter from this

A mass spectrometer similar to the one in Figure P 24.67 is...

A mass spectrometer similar to the one in Figure $\mathrm{P} 24.67$ is designed to analyze biological samples. Molecules in the sample are singly ionized, then they enter a $0.80 \mathrm{T}$ uniform magnetic field at a speed of $2.3 \times 10^{5} \mathrm{m} / \mathrm{s} .$ If a molecule has a mass 85 times the mass of the proton, what will be the approximate distance between the points where the ion enters and exits the magnetic field? A. $25 \mathrm{cm}$ B. $50 \mathrm{cm}$ C .75 \mathrm{cm}$ D. 100 cm

A mass spectrometer similar to the one in Figure $\mathrm{P} 24.67$ is designed to analyze biological samples. Molecules in the sample are singly ionized, then they enter a $0.80 \mathrm{T}$ uniform magnetic field at a speed of $2.3 \times 10^{5} \mathrm{m} / \mathrm{s} .$ If a molecule has a mass 85 times the mass of the proton, what will be the approximate distance between the points where the ion enters and exits the magnetic field?
A. $25 \mathrm{cm}$
B. $50 \mathrm{cm}$
C .75 \mathrm{cm}$
D. 100 cm

Key Concepts

Lorentz Force

The Lorentz force is the force that a charged particle experiences when moving through a magnetic field. This force is perpendicular to both the velocity of the particle and the magnetic field, resulting in the particle following a curved, typically circular path. Understanding the Lorentz force is essential for analyzing how charged particles behave within magnetic fields, which is a fundamental principle in many devices including mass spectrometers.

Circular Motion of Charged Particles

When a charged particle enters a magnetic field with its velocity perpendicular to the field, it undergoes uniform circular motion. This motion can be described with the expression r = mv/(qB), where r is the radius of the circular path, m is the mass, v is the velocity, q is the charge, and B is the magnetic field strength. This relationship is crucial for predicting the trajectory and deflection of ions in a mass spectrometer.

Mass Spectrometry

Mass spectrometry is an analytical technique used to determine the mass-to-charge ratio of ions. It operates on the principle that ions, when subjected to a magnetic field, follow trajectories that depend on their mass and charge. This allows for the separation and analysis of ions based on variations in their mass-to-charge ratios, which is fundamental in identifying and characterizing molecules in a sample.

Geometric Properties of Circular Arcs

The geometry of circular motion plays a significant role in determining distances related to the path of a charged particle. Specifically, the distance between the entry and exit points of a charged particle in a magnetic field can often be analyzed as the chord of a circular path or arc. This geometric understanding allows for the calculation of physical distances relevant in devices like mass spectrometers where ion trajectories are used to infer properties of the particles.

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