Physics

Physics · electromagnetism

Problem

A mass spectrometer consists of a pair of electrodes kept at a potential difference

\left|V_{0}\right|=1 \mathrm{MV}

, followed by a magnetic analyzer of length

L=1 \mathrm{~m}

and uniform magnetic field with intensity

|\mathbf{B}|=1 \mathrm{kG}

. Positive ions are produced at rest at the grounded electrode and accelerated by the electric field towards the cathode. The position of arrival

y

at the opposite side of the spectrometer is measured with an uncertainty

\sigma_{y}

. The beam to be composed of

{ }^{12} \mathrm{C}^{+}

and

{ }^{13} \mathrm{C}^{+}

ions in unknown proportion. What is the minimum resolution

\sigma_{y}

necessary to identify the correct mass number to better than

3 \sigma

per incident ion?