Suppose the electric field between the electric plates in...

Suppose the electric field between the electric plates in the mass spectrometer of Fig. $27-33$ is $2.48 \times 10^{4} \mathrm{~V} / \mathrm{m}$ and the magnetic fields are $B=B^{\prime}=0.58 \mathrm{~T} .$ The source contains carbon isotopes of mass numbers $12,13,$ and 14 from a long dead piece of a tree. (To estimate atomic masses, multiply by $\left.1.66 \times 10^{-27} \mathrm{~kg} .\right)$ How far apart are the lines formed by the singly charged ions of each type on the photographic film? What if the ions were doubly charged?

Key Concepts

Ion Trajectory Analysis

Ion trajectory analysis involves calculating the path of an ion as it moves through electric and magnetic fields. This typically includes equations that relate the ion's velocity, the fields' magnitudes, and the resulting radius of curvature of its path. Such analysis is fundamental in understanding how ions of different mass-to-charge ratios are spatially separated in a mass spectrometer.

Charge-to-Mass Ratio

The charge-to-mass ratio (q/m) is a crucial parameter in mass spectrometry because it determines how much an ion will be deflected by the fields. Ions with different masses or charges will have different q/m ratios, which causes them to travel along different trajectories when subject to the same electric and magnetic fields.

Effect of Ion Charge

The effect of ion charge is significant in mass spectrometry because ions with higher charges experience stronger forces in the presence of electric and magnetic fields. This leads to greater deflection of ions with higher charges compared to singly charged ions of the same mass, thereby affecting the spatial separation patterns on the detection medium.

Mass Spectrometry

Mass spectrometry is an analytical technique used to separate ions based on their mass-to-charge ratios. It involves ionizing chemical species and then subjecting them to electric and magnetic fields, which cause ions with different masses and charges to follow different trajectories, allowing for their detection and relative quantification.

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in electric and magnetic fields. It is the sum of the electrical force (from the electric field) and the magnetic force (which depends on the particle's velocity and the magnetic field). This force governs the curved paths that ions follow in devices like mass spectrometers.

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