## Related questions with answers

(a) Find the radius $R$ of the curved path for a once-ionized nitrogen atom in a mass spectrometer with $B=0.05 \mathrm{~T}$ and $V_0=10 \mathrm{kV}$, using above equation.(b)Above Equation was derived nonrelativistically. What would $R$ be if calculated relativistically? How many significant figures must you include to see the difference?

Solution

VerifiedIn mass spectrometers, the subject is ionized and then accelerated through a magnetic field. The force on the ion ($\bold{F}=q\bold{v}\times \bold{B})$ makes its path curved with radius $R$. Equation (16.44) relates the mass $m$, to the radius $R$ given constant magnetic field $B$ and potential difference $V_0$ used to accelerate the ion.

$m=\dfrac{eB^2R^2}{2V_0}\tag{16.44}$

We use this formula to determine the mass of Nitrogen atom.

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