Circular Motion in a Simple Mass Spectrometer

In summary: Bv^2 = qvB / mv = qvB / mv = sqr rt (qvB / m)deltaV = EdIn summary, the magnetic field in the simple mass spectrometer is equal to 2p/dq.
  • #1
Oribe Yasuna
43
1

Homework Statement


In the simple mass spectrometer shown in the figure below, positive ions are generated in the ion source. They are released, traveling at very low speed, into the region between two accelerating plates between which there is a potential difference ΔV. In the shaded region there is a uniform magnetic field B
rightarrowhead.gif
; outside this region there is negligible magnetic field. The semicircle traces the path of one singly charged positive ion of mass M, which travels through the accelerating plates into the magnetic field region, and hits the ion detector as shown.

Determine the appropriate magnitude and direction of the magnetic field B
rightarrowhead.gif
, in terms of the known quantities shown in the figure below (in addition to M and q, where q is the charge on an ion).

Magnitude B = ?
direction = ?

14f06f7925.png


Homework Equations


Fmag = dp/dtmag = qvB
dp/dtmag = p(v/R) = p(omega), p = ymv
omega = q_mag * b / (ym)

The Attempt at a Solution


deltaV (I don't know what to do with electrical potential)
M (mass)
q (charge)
d/2 = R (radius)
v << c, y = 1, p = mv (approximation)

Fmag = dp/dtmag
qvB = p(v/R)
qvB = p(v/(d/2))
qB = p/(d/2))
B = p/(d/2))/q
B = 2p/dq, p = mv (approx.)
B = 2Mv/dq

This is wrong, probably because I'm not given velocity. However, I don't know how to get magnetic field without velocity? I think the problem is I don't know what to do with electric potential.
 
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  • #2
Your ion with charge q is accelerating through the ΔV between the plates. Look for an equation relating the energy acquired by an electric charge accelerating through a potential difference.
 
  • #3
1/2 mv^2 = q deltaV

This kinetic energy equation?

mv^2 = 2q deltaV
v^2 = 2q deltaV / m
v = sqr rt (2q delta V / m)
 
  • #4
deltaV = Ed

But I'm missing both E and d? d is the separation between the plates but the variable d in the image seems to be a length.
 
  • #5
Oribe Yasuna said:
deltaV = Ed

But I'm missing both E and d? d is the separation between the plates but the variable d in the image seems to be a length.
There's another equation that involves the charge.
 

Related to Circular Motion in a Simple Mass Spectrometer

1. What is circular motion in a simple mass spectrometer?

Circular motion in a simple mass spectrometer is the movement of charged particles in a circular path within a magnetic field. This is used to separate and analyze particles based on their mass-to-charge ratio.

2. How does a simple mass spectrometer work?

A simple mass spectrometer works by ionizing a sample, accelerating the ions using an electric field, and then steering them into a circular path using a magnetic field. The ions are then detected and analyzed based on their mass-to-charge ratio.

3. What is the purpose of circular motion in a mass spectrometer?

The purpose of circular motion in a mass spectrometer is to separate ions based on their mass-to-charge ratio. Since the radius of the circular path is dependent on the mass-to-charge ratio, lighter ions will have a larger radius and heavier ions will have a smaller radius, allowing for their separation.

4. What factors affect the circular motion in a mass spectrometer?

The strength of the electric and magnetic fields, as well as the mass and charge of the ions, can affect the circular motion in a mass spectrometer. Additionally, external factors such as temperature and pressure can also impact the motion of the ions.

5. What are some applications of circular motion in a mass spectrometer?

Circular motion in a mass spectrometer is commonly used in scientific research, particularly in the fields of chemistry, physics, and biology. It is also used in various industries such as pharmaceuticals, forensics, and environmental sciences for analyzing and identifying compounds and molecules.

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