Chapter 26.1, Problem 11SSC

To determine

To check: The methods in which the mass spectrometer’s magnetic field have to be changed for the ions to hit the detector.

Answer to Problem 11SSC

For different ions to hit the photographic film, the magnetic field in the spectrometer should be adjusted in proportional to the square root of the mass of the ions.

Explanation of Solution

Formula used:

Expression of the radius of the circular path followed by an ion in the spectrometer is

  $r=\frac{mv}{qB}$…… (1)

Velocity of an undeflected ion can be expressed as

  $v=\sqrt{\frac{2qV}{m}}$…… (2)

Here, $v,m,B,q$ and $V$ are velocity of the ion, mass of the ion, magnetic field strength, charge of an ion and potential different between anode and cathode.

Calculation:

Substitute $\sqrt{\frac{2qV}{m}}$ for $v$ in equation (1)

  $r=\frac{m}{qB}\times \sqrt{\frac{2qV}{m}}$

  $B=\sqrt{\frac{2Vm}{q{r}^2}}$…… (3)

If constant acceleration voltage is used for similarly charged ions and if these ions should have same path radius, then this equation gives

  $B\propto \sqrt{m}$  ...... (4)

This means that the magnetic field in the spectrometer will be balanced proportionally to the square root of the ion mass for the various ions to enter the photographic film. For example, if the mass of an ion increases by a factor of 400. Then the magnetic field should be increased by a factor of 20.

Conclusion:

Hence, for different ions to hit the photographic film, the magnetic field in the spectrometer should be adjusted in proportional to the square root of the mass of the ions.