Question

A mass spectrometer is a device for separating particles of different masses from a mixture. For example, the technology is used to investigate qualitative and quantitative changes within thousands of biologically active components such as proteins, lipids and metabolites. A mass spectrometer consists of three sections:

• The accelerator
• The velocity selector
• The magnetic chamber

(1) Accelerator (acc): In the accelerator, there is only an uniform Electric field due to a potential difference Vacc across two vertical plates separated from a distance dacc. This E-field, Eacc, accelerates the charged particles. The charge emerges from the vertical plates with a speed v.

Skecth the situation describing the accelerator.

What are the EQUATIONS defining:

• the E-field between the plates, Eacc
• the acceleration acting on the charge, charge.acc
• the position as the charge travels, charge.pos
• the velocity as the charge travels, charge.v

(2) Velocity Selector (sel): In the velocity selector, there are two uniform fields: an Electric field, Esel, and a Magnetic field, Bsel, perpendicular to each other. Only the charges with a specific speed will be able to move undeflected between the two horizontal plates.

Sketch the situation describing the velocity selector.

What are the EQUATIONS defining:

• the E-field between the plates, Esel
• the electric force acting on the charge
• the magnetic force acting on the charge
• the total force acting on the charge, Fsel
• the acceleration on the charge, charge.acc
• the position as the charge travels, charge.pos
• the velocity as the charge travels, charge.v
• the momentum of the charge from velocity, charge.momentum

(3) Magnetic Chamber (cham): In the magnetic chamber, there is only an uniform magnetic field, Bcham. Once the undeflected charges reach the chamber, they will rotate in the field until they hit a detector.

Sketch the situation describing the magnetic chamber.

What are the EQUATIONS defining:

• the force acting on the charge, Fmag
• the momentum of the charge from the force, charge.momentum
• the velocity as the charge travels, charge.v
• the position as the charge travels, charge.pos
• How can you find the radius of curvature from the above information?

Look at this: simulation

Singly charged positive ions (m = 5.80E-26 kg) are introduced into a mass spectrometer. The ions are first accelerated by the electric field established by placing a potential difference Vacc = 20.0 V across the vertical plates distanced by 2.0 cm. Next, they pass through the horizontal plates of a velocity selector, Vsel = 52.5 V spaced by 1 cm and placed in a uniform magnetic field, Bsel = 0.500 T (-k). Finally they enter a region where a uniform magnetic field of Bcham = 0.200 T (+k) exists.

Sketch the whole situation.

Determine the following:

a) The speed of ions entering the velocity selector.

b) What must be the direction of Esel for the ions to be undeflected?

c) The radius of curvature of the ions in the B-chamber.

Answer 1

accelerator:

• the E-field between the plates, Eacc = V/d_acc
• the acceleration acting on the charge, charge.acc = E_acc *q/m
• the position as the charge travels, charge.pos = charge.acc *t²/2
• the velocity as the charge travels, charge.v = charge.acc *t

mass of the ion m = 5.28E-26 kg

Pot. diff = 20 V. Plates gap d=2.0cm

electric field E= V/d = 20/0.02 = 2000 V/m

acceleration a = Ee /m

speed of the ion at the end v² = 2ad  

v= sqrt( 2*2000*(1.6E-19/5.28E-26) * 0.02) = 1.56E+5 m/s

b) E_sel must be perpendicular to B_sel ( -k ) , say j, we take i , vel. direction of the ions

c) radius of curvature

R = mv/Bq = 5.28E-26 * 1.56E+5 / 0.2 * 1.6E-19 = 25.74 cm