Question

need some help deriving an equation for the mass of an ion in a mass spectrometer in terms of voltage, magnetic field strength, radius of particle deflection, and charge

Answer 1

I am given:

qvB = mv^2/r

qV = (1/2)mv^2

the sol'n is m = \(\frac{ qB^2*r^2 }{ 2V }\)

I feel like I'm missing something obvious but I can't quite get that solution

Answer 2

\(qvB = \frac{mv^2}{r}\)
\(qV = (1/2)mv^2\)
\(v^2=\frac{2qV}{m};\)
\(qvB=\frac{m(2qV/m)}{r}=2qV/r\)
\(vB=\frac{2V}{r}\)
\(v=\frac{2V}{rB}\)
\(qV=(1/2)mv^2\)
\(\frac{2qV}{v^2}=m\)
\(m=\frac{2qV}{(\frac{2V}{rB})^2}=\frac{2qVr^2B^2}{4V^2}=\frac{qB^2r^2}{2V}\)
\(\text{as desired}\)

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Answer 3

@Vocaloid

Answer 4

thank you

Answer 5

Look I owe you an apology for being obnoxious. I will do better.