Chapter 26.1, Problem 9SSC

To determine

To Explain: The process in which a mass spectrometer can separate ions of different masses using the equation $r=\frac{1}{B}\sqrt{\frac{2V_{accel}m}{q}}$ .

Explanation of Solution

Introduction:

J.J. Thomson did experiment to determine the charge-to-mass ratio of electrons i.e. $\left(\frac{q}{m}\right)$ . By knowing $\left(\frac{q}{m}\right)$ and charge of an electron, one can determine the mass of an electron. Thomson conducted experiments to demonstrate that atoms consisted of subatomic particles with both positive and negative charges. He determined that the particles charged negatively are much lighter than the particles charged positively.

The sample containing the atom is injected into an instrument which is called a mass spectrometer. The samples are vaporized by the heat.

High energy electrons bombard the vaporized sample that knock out a sample electron and positive charged ions are produced. Then these ions are accelerated by electrical plates, and then deflected by a magnetic field.

In this case, the ions that are heavier and moving slowly are deflected less, while ions that are lighter and moving fast are deflected more. This is evident from the equation of radius of the circular path of ion i.e. $r=\frac{1}{B}\sqrt{\frac{2V_{accel}m}{q}}$ i.e.

In this case, the radius is proportional to the square root of the mass/charge ratio.

The electric field often deflects ions that have higher charges rather than ions with smaller charges. The amount by which each ion deflects is inversely related to its mass-to-charge ratio, $\left(m/q\right)$ .

Here  m  is equal to the mass of the ion and  q  is equal to its charge.

When it deflected, the ions hit a mass spectrometer detector.

Conclusion:

Hence, the deflection of ions of different masses using mass spectrometer depends on the mass by charge ratio.