Question

A doubly-ionized lithium ion with a charge of +2e has a direction that is perpendicular to the 0.630-T magnetic field inside a mass spectrometer as it enters the field. The ion has a mass m = 9.98811 x 10⁻²⁷ kg and a kinetic energy KE = 3.24 x 10⁻¹⁶ J. Determine the radius, in meters, of the path the ion follows in the magnetic field.

Answer 1

The question involves calculating the radius of the circular path followed by a doubly-ionized lithium ion in a magnetic field of a mass spectrometer. The formula for finding radius, given the ion's mass, charge, magnetic field strength, and kinetic energy, can be applied to derive the required value.

Step-by-step explanation:

The student is asking about the path a doubly-ionized lithium ion with a charge of +2e takes when it enters a mass spectrometer's magnetic field. The Li2+ ion, with a known mass and kinetic energy, moves perpendicular to a uniform magnetic field. To determine the radius of the circular path the ion follows, one can use the formula r = mv/qB, where m is the mass of the ion, v is the velocity, q is the charge, and B is the magnetic field strength.

First, we need to find the velocity of the ion using its kinetic energy with the formula KE = 0.5mv2. After calculating the velocity, the radius can be found using the above formula. By calculating the radius, you will understand the circular path that a charged particle follows under the influence of a magnetic field, which is a cornerstone concept in magnetic force and motion in magnetic fields.

In the context of mass spectrometry, this movement and the resulting radius are critical for identifying ions based on their mass-to-charge ratios.