Mass spectrometer radius curvature

[deleted783484]

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How come a particle with larger mass has a greater radius of curvature? I know that the equation shows that r= mv/qB so if m increases r increases but if a particle is heavier it deflects less so shouldn't the radius of curvature be smaller?

Thanks!

 

[babyoreo]

The radius of curvature is the radius of the (circular) path the object will take. Since the heavier object resists the centripetal force pulling it into a circular path given its larger mass ("deflects less") it will travel in a large circular path, as opposed to a tighter circle. Therefore, the radius of curvature will be relatively large.

 

[deleted783484]

The radius of curvature is the radius of the (circular) path the object will take. Since the heavier object resists the centripetal force pulling it into a circular path given its larger mass ("deflects less") it will travel in a large circular path, as opposed to a tighter circle. Therefore, the radius of curvature will be relatively large.

I'm sorry but this still doesn't make sense to me. I attached a sketch of how I see the deflection with A having a larger mass than B so A is deflecting less and in my figure I see that the radius for A (heavier) is smaller than B.

Thanks again!

 

[jparsenal87]

It seems like you have this a little backwards. In your picture, what it REALLY looks like you have is:

1. A being subjected to a centripetal force F, caused by a magnetic field.

2. B continuing in a straight line for a period (meaning its subjected to no force), THEN being subjected to the same force F (I say this because it LOOKS like the radius of your actual curving portion for both A and B is similar).

Of course the reality is that both particles are subjected to the same uniform magnetic field at the same time - so your curves should begin at the same point. But A (the heavier one) should be deflected LESS, not more. You seem to have the general idea, but just flipped. Assuming that your drawing just had 2 circles, B would be the one being deflected less, having the higher r, and being more massive.

Hope this makes some bit of sense.

 

[aldol16]

Think about it this way. You release two particles at the same time and they fly in a straight line. A is bigger than B. Then, you apply an equal force on each of the the particles, trying to deflect it so that it curves. Since you're applying equal force and F = m*a, which particle will experience the largest acceleration. The particle that experiences the largest acceleration will curve more and thus hit the side first. The particle that experiences the smallest acceleration will curve the least with application of force and will thus hit the side last.

 

[jparsenal87]

Think about it this way. You release two particles at the same time and they fly in a straight line. A is bigger than B. Then, you apply an equal force on each of the the particles, trying to deflect it so that it curves. Since you're applying equal force and F = m*a, which particle will experience the largest acceleration. The particle that experiences the largest acceleration will curve more and thus hit the side first. The particle that experiences the smallest acceleration will curve the least with application of force and will thus hit the side last.

Was curious about this because I always see 2 reasons for the decreased deflection, and I'm just curious if my logic is off. The first is exactly like yours - equal force means lower acceleration for the more massive object. For the second, I came across a practice problem that discussed particles being accelerated from rest across a potential difference V. In this case, the PE=qV is converted to KE=1/2mv^2, so the more massive object should have a lower velocity upon entering the mass spec. By that logic, lower velocity should correspond to lower force applied by the magnetic field (F=qvB), so less force means less deflection. Is this also true, or am I making an error in my logic somewhere?

 

[aldol16]

Was curious about this because I always see 2 reasons for the decreased deflection, and I'm just curious if my logic is off. The first is exactly like yours - equal force means lower acceleration for the more massive object. For the second, I came across a practice problem that discussed particles being accelerated from rest across a potential difference V. In this case, the PE=qV is converted to KE=1/2mv^2, so the more massive object should have a lower velocity upon entering the mass spec. By that logic, lower velocity should correspond to lower force applied by the magnetic field (F=qvB), so less force means less deflection. Is this also true, or am I making an error in my logic somewhere?

Good question. Look up velocity selector.

 

[jparsenal87]

Good question. Look up velocity selector.

Makes total sense. Thanks so much!

 

[babyoreo]

I'm sorry but this still doesn't make sense to me. I attached a sketch of how I see the deflection with A having a larger mass than B so A is deflecting less and in my figure I see that the radius for A (heavier) is smaller than B.

Thanks again!View attachment 214119

You have it backwards. Deflection = deviation from the normal path. Less deflection = less deviation = less "curviness" = larger circles.

These ions are initially traveling in a straight line. Due to the magnetic field, an equal force acts on each ion. The heavier ions (purple) are accelerated less due to their higher mass. Therefore, they are deflected less, and follow a trajectory with a larger radius (imagine if these trajectories formed a circle: the purple circle will be larger (larger radius r) and the green circle will be smaller (smaller radius r).

Was curious about this because I always see 2 reasons for the decreased deflection, and I'm just curious if my logic is off. The first is exactly like yours - equal force means lower acceleration for the more massive object. For the second, I came across a practice problem that discussed particles being accelerated from rest across a potential difference V. In this case, the PE=qV is converted to KE=1/2mv^2, so the more massive object should have a lower velocity upon entering the mass spec. By that logic, lower velocity should correspond to lower force applied by the magnetic field (F=qvB), so less force means less deflection. Is this also true, or am I making an error in my logic somewhere?

Yes, the logic for the second explanation makes sense as well.

 

[deleted783484]

You have it backwards. Deflection = deviation from the normal path. Less deflection = less deviation = less "curviness" = larger circles.

These ions are initially traveling in a straight line. Due to the magnetic field, an equal force acts on each ion. The heavier ions (purple) are accelerated less due to their higher mass. Therefore, they are deflected less, and follow a trajectory with a larger radius (imagine if these trajectories formed a circle: the purple circle will be larger (larger radius r) and the green circle will be smaller (smaller radius r).



Yes, the logic for the second explanation makes sense as well.

It finally makes sense I wasn't understanding what deflection meant! Thanks a lot!!