Question

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an ele. 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 the ion) / (mass of the ion)] will be proportional to. 

(a) (1/r²) 

(b) r² 

(c) r 

(d) (1/r)

Answer 1

The correct option (a) (1/r²)

Explanation:

We know

Magnetic force = centripetal force

∴ qVB = (mV² / r)

∴  r = (mV / qB)

also KE = (1/2)mV² i.e.   E_k = (1/2)mV²

∴  V = √[(2E_k) / m]

 ∴   r = [√(2E_km) / qB]

also KE = E_k = q ∙ V

∴ r = [√(2mqV) / qB]

∴  r²B²q² = 2mqV

∴  (q/m) = [(2V)/(B²r²)]

i.e.   (q/m) ∝ [1/(radius)²]