9.0 Mass spectrograph

  Magnetics

It is used to find mass number, to determine the relative abundance of isotopes or to produce separated isotopes. An instrument in which we use a photographic plate and obtain a series of lines on it are known as mass spectrographs. Another instrument in which an electric or magnetic field is adjusted to make each part of the spectrum in turn to fall on a fixed detecting slit and measured electrically are called mass spectrometers. All mass spectroscopes start with an ion source where the ions are produced by electron bombardment of gases. The ions are first set in motion with the help of an accelerating potential. In the spectrograph designed by Bainbridge, a velocity selector is used to obtain ions of particular velocity $v.$ The velocity selector allows a beam of a positive ion having the same velocity $v$ to pass undeviated through crossed electric and magnetic fields $\vec E$ and $\vec B.$ In this case forces due to these fields are equal and opposite. i.e., $F_e=F_m$

$$qE = qvB$$$$v = \frac{E}{B}\quad \quad .....\left( i \right)$$

All the ions having the same velocity, $v = \frac{E}{B}$ enter the analysing chamber through slit. In this chamber, another magnetic field $B$ is applied perpendicular to the plane of paper and in outward direction. Due to this field, ions of different masses move in circles of different radii such that$$\frac{{m{v^2}}}{r} = qvb'$$$$m = \frac{{qrb'}}{v}\quad \quad .....\left( {ii} \right)$$Assuming equal charges on each ion, the mass of each ion is proportional to the radius of its path. Ions of different isotopes converse at different points on the photographic plate. The relative abundance of the isotopes is measured from the densities of the photographic images they produce. For two isotopes of masses $m_1$ and $m_2,$ we have$$\frac{{{m_1}}}{{{m_2}}} = \frac{{{r_1}}}{{{r_2}}}.$$