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 path 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

Options

(a) 1/R²
(b) R²
(c) R
(d) 1/R

Correct Answer:

1/R²

Explanation:

In mass spectrometer, when ions are accelerated through potential V
1/2 mv² = qV …..(i)
As the magnetic field curves the path of the ions in a semiciruclar orbit
Bqv = mv² / R v = BqR / m ….(ii)
Substituting (ii) and (i)
1/2 m[ BqR / m]² = qv or q/m = 2V / B²R²
Since V and B are constants, q/m ∞ 1/R²