Figure below shows the essentials of a mass spectrometer which is used to measur

Question

Figure below shows the essentials of a mass spectrometer which is used to measure the masses of ions. An ion of mass m and charge +q is produced in source S a chamber in which a gas discharge is taking place. The initially stationary ion leaves S, is accelerated by a potential difference V, and then enters a separate chamber in which there is a magnetic field B. In the field it moved in a semicircle striking a photographic plate at distance X from the entry point. Show that the ion mass m is given by: m = B^2 q / 8V X^2

Explanation / Answer

energy equation:

(1/2)mv2 = qV
v2= 2qV/m

In the magnetic field
F = qvB = mv2/r
m = qrB/v = qrB. (m/2qV)
m2 = q2 r2 B2 m/(2qV)
m = q B2 r/(2V)
r = x2
m = q B2 x2/(8V)

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