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Tina20
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Homework Statement
The image below shows a mass spectrometer, an analytical instrument used to identify the various molecules in a sample by measuring their charge-to-mass ratio e/m. The sample is ionized, the positive ions are accelerated (starting from rest) through a potential difference ΔV, and they then enter a region of uniform magnetic field. The field bends the ions into circular trajectories, but after just half a circle they either strike the wall or pass through a small opening to a detector. As the accelerating voltage is slowly increased, different ions reach the detector and are measured. Typical design values are a magnetic field strength B=0.243 T and a spacing between the entrance and exit holes d=7.30 cm. What accelerating potential difference ΔV is required to detect N2+?
Homework Equations
f=qB/2(pi)m
f=frequency
m=mass of N2+ = 2x14.0031u
u=1.661x10-27
therefore mass of N2 = 2x14.0031x1.661x10-27 = 4.6518x10-26
T=1/f
T=v/2(pi)r
1/2mv^2 = qV
The Attempt at a Solution
f=qB/2(pi)m
f=(1.602x10-19)(0.243)/2(pi)(4.6518x10-26)
f=133,188.0004 Hz
T = 1/f
T= 1/133,188.0004 Hz
T=7.50818x10-6s
T=v/2(pi)r
T=v/2(pi)(d/2)
7.50818x10-6s = v/2(pi)(0.0730/2)
v=1.72189x10-6m/s
1/2mv^2 = qV
1/2(4.6518x10-26kg)(1.72189x10-6m/s)^2 = (1.602x10-19C)V
4.304x10-19 = V
The answer is wrong and I have no idea any other way to solve this. Some guidance would be very helpful!
Tina