How Does Magnetic Field Strength Affect Ion Trajectory in a Mass Spectrometer?

[k4s11]

A mass spectrometer, sketched below, is a device used to separate different ions. Such ions with a well-defined velocity Vo enter through a slit into a region of uniform magnetic field B, where they follow a semicircular path until they strike the detector slit above the entry slit. The distance between the entry and the detector slits is d = 1.30 m.

1. [1pt]
Chlorine ions of mass 35 amu (1 amu equals 1.66x10-27 kg), carrying a charge of +1e, enter the spectrometer with initial speed of vo = 3.40E5 meters/sec. What value of B is required for these ions to hit the detector?

Answer: Last Answer: -.095 T
Incorrect, tries 4/99.

I tried: r=mv/(qB) => B= mv/(qr)

B= (5.81 x 10^-26 kg x 3.40 x 10^5 m/s) / (1.60 x 10^-19 C x 1.30 m)
B= .0950 T

where did i go wrong?

 

[Gear300]

If I'm picturing the situation right, d = 1.30 m is the diameter. The radius is explicitly needed in your equations.

 

[baba89]

Your calculation is correct. The only potential error is in the conversion of units. Make sure to use consistent units throughout your calculation, and convert to the appropriate units before plugging them into the equation. In this case, make sure to convert the mass from amu to kg and the velocity from m/s to m/s before solving for B. Also, remember to use the correct charge for the ion, which is +1e or 1.60 x 10^-19 C, not 1 C.