# Double focusing mass spectrograph

A double focusing mass spectrograph is an instrument which uses both directional and velocity focusing. In this spectrograph, an electrostatic energy filter of 127º and a magnetic momentum filter are employed. When the angle of the sector magnet is 60º, the resulting velocity dispersion by energy filter is just annulled by momentum filter.

A schematic diagram of this spectrograph is shown in fig. This type of spectrograph was first made by Bainbridge and Jordan in 1936.

## Theory

Ions are produced in a high voltage (20 KV) low current discharged tube which is filled with the desired gas at low pressure. A beam of ions emerges from the cathode side S1 of the discharge tube and enters through a slit S2 into a cylindrical electrostatic energy filter E maintained ar a good high vacuum pressure 10mm of Hg. It consists of a pair of cylindrical plates of the radius of curvature 25cm. A proper voltage is applied between the plates so that only ions of prescribed values of kinetic energy should emerge through the slit S3. And other ions should stop by the filter.

The ions emerging from the slit S3 are then analyzed by the magnetic filter M into different mass species. The ions emerging from the magnetic filter have the same momentum. Each component is focused as a line trace on the photographic plate P. The exit slit of energy filter, the apex of the magnet and the photographic plate are collinear. The positions of line trace on the photographic plates are proportional to the mass of the atoms. By measuring the positions of the spectral lines with the position of the known mass reference line, one can determine the mass of the given atoms.

### Advantage

This spectrograph can measure atomic masses very accurately as it has the following advantage.

- The mass spectrum across the photographic plate is almost linear.
- It has a resolving power of the order of 10⁴.
- The simultaneous focusing of velocity and direction results in linear marks drawn on the photographic plate in higher intensities.

Although the sensitivity of this mass spectrographs is quite high, yet its sensitivity cannot be increased beyond a certain limit due to the limited contrast of a photographic emulsion. Due to this reason, masses of isotopes available in the least quantity cannot be determined by the spectrograph.

#### Example:

1. In a cylindrical electrostatic energy filter, the distance between the plates is 10cm and radius of curvature is 10m. On applying the 20000V potential difference between the plates, singly charged Na ions are passed between the plates. Determine the kinetic energy of ions emerging from the filter.

Solution: The kinetic energy of the Na+ emerging from energy filter,

E= neVR/2d

Given : n = 1 ; e = 1.6×10⁻¹⁹ C : V= 20,000 volt

R= 5m ; d = 10cm = 0.1 m

E= 1×1.6×10⁻¹⁹×20,000×5/2×0.1 = 8×10⁻¹⁴ J

E= 8×10⁻¹⁴/ 1.6×10⁻¹³ = 0.5 MeV

##### 2. In a cylindrical electrostatic energy the distance between the plates is 5cm and radius of curvature is 5m. How much potential diffrence is applied between the plates, so that C++ ions of energy 1MeV emerged from the filter?

solution : The kinetic energy of the C++ emerging from energy filter,

E =neVR/ 2d

or V= 2dE/neR

Given n= 2 ; e= 1.6×10⁻¹⁹ C ; E= 1MeV = 1.6×10⁻¹³J

R= 5m ; d= 5cm = 0.05m

V = 2×0.05×1.6×10⁻¹³/ 2×1.6×10⁻¹⁹×5

V = 10,000 Volt

###### 3. In momentum filter the magnetic field of sector magnet is 0.1 T. And radius of curvature of sector magnet is 2m. find the kinetic energy of these ions emerging from it When doubly charged C ions are passed through it

Solution: The kinetic energy of the ions passing through the momentum filter

E= (neBR)²/2M

Given n=2 , e= 1.6×10⁻¹⁹ C ; B= 0.1 T ; R= 2 m

M= 12×1.67 ×10⁻²⁷ kg

E= (2×1.6×10⁻¹⁹×0.1×2)²/ 2×12×1.67×10⁻²⁷ = 1.02 ×10⁻ J

E= 1.02 × 10/ 1.6 ×10 = 0.64 MeV

###### Conclusion

In this particular article Double Focusing Mass Spectrograph, we have studied the basic introduction of Double Focusing Mass Spectrograph and its theory and working. We have also discussed some numerical based on Double Focusing Mass Spectrograph in the easiest way possible.