The isotopes magnesium-24 (mass (3.983 times 10^{-26} mathrm{~kg}) ) and magnesium-26 (mass (4.315 times 10^{-26} mathrm{~kg}) )


The isotopes magnesium-24 (mass \(3.983 \times 10^{-26} \mathrm{~kg}\) ) and magnesium-26 (mass \(4.315 \times 10^{-26} \mathrm{~kg}\) ) are to be separated using a mass spectrometer in which the magnetic field magnitude is \(0.577 \mathrm{~T}\). The ions used are the ones that have lost one electron each, \({ }^{24} \mathrm{Mg}^{+}\)and \({ }^{26} \mathrm{Mg}^{+}\). What is the minimum value of the potential difference through which these ions must be accelerated if the separation distance between them on the detector screen must be \(2.60 \mathrm{~mm}\) ? (Assume the mass ratio is \(26 / 24\).)

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