In a mass spectrometer used for measuring the masses of...

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an ele. potential $\mathrm{V}$ and then made to describe semicircular paths of radius $\mathrm{r}$ using a magnetic field $\mathrm{B}$. If $\mathrm{V}$ and $\mathrm{B}$ are kept constant, the ratio [(Charge on the ion) / (mass of the ion)] will be proportional to. (a) $\left(1 / r^{2}\right)$ (b) $r^{2}$ (c) $\mathrm{r}$ (d) $(1 / \mathrm{r})$

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an ele. potential $\mathrm{V}$ and then made to describe semicircular paths of radius $\mathrm{r}$ using a magnetic field $\mathrm{B}$. If $\mathrm{V}$ and $\mathrm{B}$ are kept constant, the ratio [(Charge on the ion) / (mass of the ion)] will be proportional to.
(a) $\left(1 / r^{2}\right)$
(b) $r^{2}$
(c) $\mathrm{r}$
(d) $(1 / \mathrm{r})$

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Key Concepts

Kinetic Energy from Electric Potential

When ions are accelerated through an electric potential difference, their electrical potential energy is converted into kinetic energy. The relationship ½ m v² = qV connects the ion's mass, charge, and the voltage applied, establishing the foundation for determining its velocity before it enters the magnetic field.

Lorentz Force and Circular Motion

In a magnetic field, a moving ion experiences a Lorentz force that acts perpendicular to its velocity, causing it to follow a curved or circular path. Equating the magnetic force (qvB) with the centripetal force (m v²/r) reveals how the ion's velocity, mass, charge, magnetic field strength, and radius of the path interrelate.

Mass Spectrometry Principle

Mass spectrometry utilizes the principles of ion acceleration and magnetic deflection to separate ions based on their mass-to-charge ratios. By measuring the radius of curvature of an ion's path in a magnetic field, one can infer the charge-to-mass ratio, which is central to identifying the ion's properties in analytical applications.

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