Question

34. In a mass spectrometer used for measuring the
masses of ions, the ions are initially accelerated by
an electric potential V and then made to describe
semicircular paths of radius R using a magnetic field
B. If V and B are kept constant, the ratio
charge on theion
mass of theion
will be proportional to
[AIPMT (Prelims)-2007]
co​

Answer 1

We know Magnetic force = centripetal force ∴ qVB = (mV2 / r) ∴ r = (mV / qB) also KE = (1/2)mV2 i.e. Ek = (1/2)mV2 ∴ V = √[(2Ek) / m] ∴ r = [√(2Ekm) / qB] also KE = Ek = q ∙ V ∴ r = [√(2mqV) / qB] ∴ r2B2q2 = 2mqV ∴ (q/m) = [(2V)/(B2r2)] i.e. (q/m) ∝ [1/(radius)2]

proportionak to 1/R^2