After being accelerated through a potential difference of 5.0 kV, a singly charged carbon ion (

step 1 5. This given problem potential difference accelerating the charge particle that is given as v i

After being accelerated through a potential difference of...

After being accelerated through a potential difference of $5.0 \mathrm{kV}$, a singly charged carbon ion $\left({ }^{12} \mathrm{C}\right)$ moves in a circle of radius $21 \mathrm{~cm}$ in the magnetic field of a mass spectrometer. What is the magnitude of the field?

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Key Concepts

Energy Conversion in Charged Particle Acceleration

When a charged particle is accelerated through an electric potential difference, the work done by the electric field converts into kinetic energy. Specifically, for a particle with charge q accelerated through a potential difference V, the kinetic energy acquired is given by qV. This principle is fundamental in determining the speed of the particle before it enters a magnetic field.

Magnetic Force and Uniform Circular Motion

A charged particle moving in a magnetic field experiences a force perpendicular to its velocity due to the Lorentz force, which causes it to move in a circular path. The magnetic force, given by qvB, acts as the centripetal force needed to keep the particle in circular motion, and is set equal to m*v^2/r to relate the particle’s mass, velocity, charge, magnetic field strength, and radius of the circular path.

Mass Spectrometry and Charge-to-Mass Ratio Determination

Mass spectrometry utilizes the deflection of charged particles in magnetic fields to measure their mass-to-charge ratios. By analyzing the curvature of the particle’s trajectory in the magnetic field, and applying principles of energy conversion and circular motion, the charge-to-mass ratio of the ion can be deduced, which is essential for identifying and characterizing the ion species.

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