Figure 8.31 shows a schematic version of a mass spectrograph of K. T. Bainbridge

Question

Figure 8.31 shows a schematic version of a mass spectrograph of K. T. Bainbridge. It is a modification of the design of Fig. 8.30 because it includes a velocity selector in the vacuum chamber through which the positive ions pass. The selector uses a horizontal E field and the same B field that bends the path of the ions in the spectrograph proper. What is the mass of the ions that impinge on the photographic plate a distance s from the slit? [Answer: M = eB2s/2E] FIGURE 8.30 Exercise 6. The Dempster mass spectrograph. FIGURK 8.31 Exercise 7. The Bainbridge mass spectrograph.

Explanation / Answer

The speed of the ions is maintained by the velcoity selector by electric and magnetic field               F = B e V              - magnetic force               F = e E            electric force both the forces are equal              BeV = eE speed of the ion is              V = E / B ......(1) Now after the ion enters the ionization chamber, the centripetal force that causes it move in circular path is provided by magnetic field          F = MV^2 / (s/2)          F = BeV equating them        MV^2 / (s/2) = BeV           M = Bes / 2V    substituting equation (1)        M = B e s / 2 (E/B)            = eB^2 s /2E proved.              

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