The isotopes magnesium-24 (mass: 3.983 x 10^-26) and magnesium-26 (mass: 4.315 x

Question

The isotopes magnesium-24 (mass: 3.983 x 10^-26) and magnesium-26 (mass: 4.315 x 10^-26) are to be separated using a mass spectrometer in which the magnetic feild magnitude is .577 T. The ions are the ones that have lost one electron each, 24Mg+ and 26Mg+. 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 scren must be 2.6mm? (Assume the mass ratio is 26/24)

The anser is 678V, but can someone gives the steps to why?

Explanation / Answer

given,

mass ratio = 26/24

so mass to charge ratio will be = m/q = 1.54 x 10-9

r = 2.6 mm = 0.0026 meters

B = 0.577 Tesla

We know that,

m/q = (B r )2 / 2V

we get, V =  (B r )2 / 2(m/q) = (0.577 x 0.0026)2 / 2 x 1.54 x 10-9

V = 6.809 x 102 V = 680V

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