Using Magnetic Field to get Radius

[red99]

Homework Statement

: It is possible to accelerate atoms that have been ionized to a known kinetic energy in an electric field. Sometimes chemists and physicists are interested in identifying the chemical elements in a beam of ions all having the same kinetic energy by determining the mass of each ion in the beam. This can be achieved by bending the ion beam in a uniform magnetic field and seeing what radius the semicircular path of each of the ions has. A device that does this is called a mass spectrometer. A schematic of a mass spectrometer is shown in the diagram below.

Boron is the fifth element in the periodic table so it always has 5 protons. However, different isotopes of boron have 3, 5, 6, 7, or 8 neutrons in addition to the 5 protons to make up Boron-8, Boron-10, Boron-11, etc. As a research chemist for the Borax Company you have been asked to use a mass spectrometer to determine the relative abundance of different isotopes of boron in a sample of boron obtained from a mine near Death Valley in California. You decide to accelerate a beam of singly-ionized boron ions that have each lost one of their orbital electrons and have one unit of positive net charge (which has the same magnitude as the charge on the electron).

You decide to use an accelerating potential difference of ¬–2.68103 volts. The boron beam then enters a uniform magnetic field that has a direction perpendicular to the boron beam. You set up your electromagnet so its magnetic field has a magnitude 0.182T. You observe two bright spots on your photographic plate with the spot corresponding to a radius of 13.0 cm having four times the intensity of the one corresponding to a radius of 13.6 cm. There are very faint spots at 11.6 cm, 14.2 cm, and 14.8 cm. which isotope of boron has approximately 80% abundance? Which one has about 20% abundance? Which ones are present in only trace amounts? Please show all your reasoning and calculations.

Homework Equations

v=rq, F=qvXB, ke=1/2mv^2

The Attempt at a Solution

I have honestly been fumbling around with these equations for hours and can't seem to get anything to work. Any help would be greatly appreciated.

 

[zachzach]

So the atoms are traveling in a semi circle and $$\vec{F_{net}} = q\vec{v} \times \vec{B} = qvsin\theta = ma$$

Where $$\theta$$ is the angle between $$\vec{v}$$ and $$\vec{B}$$

It is traveling in a circle so what is a?