Radii of paths followed by particles in a magnetic field

[Jimmy25]

Homework Statement

Chlorine has two stable isotopes, 35Cl and 37Cl. Chlorine gas which consists of singly ionized ions is to be separated into its isotopic components using a mass spectrometer. The magnetic field strength in the spectrometer is 1.2 T. What is the minimum value of the potential difference through which these ions must be accelerated so that the separation between them, after they complete their semicircular path, is 1.1 cm?

Homework Equations

r = mv/qB

The Attempt at a Solution

Using the difference in the radii of the semicircles I found the velocity of the particles to be 6.36*10^7 m/s which does not seem correct.

Even if I assume the velocity is correct how do I find the potential difference through which the particle was accelerated?

 

[Redbelly98]

The Attempt at a Solution

Using the difference in the radii of the semicircles I found the velocity of the particles to be 6.36*10^7 m/s which does not seem correct.

0.2c does seem too high to be correct. But without seeing your actual calculation, it is difficult to say where your mistake is. What did you have for r, m, q and B?

Even if I assume the velocity is correct how do I find the potential difference through which the particle was accelerated?

You can think of electric potential as the energy per unit charge gained by a charged particle. Which form of energy is related to velocity, and what is that relation?

 

[Jimmy25]

You can think of electric potential as the energy per unit charge gained by a charged particle. Which form of energy is related to velocity, and what is that relation?

KE = 1/2mv²

So let V=KE/q

Now how do I determine the voltage required? the two particles do not have the same mass.

 

[Redbelly98]

You can solve for v in terms of V, and substitute back into r = mv/qB. You will end up with r in terms of m, V, and other fixed parameters.

 

[Jimmy25]

Ugghhhhh.

I don't get it. The two particles have different masses but yet I have to solve for a single potential difference.

I don't have an actual r value all I have is the difference. So I have to sub back into the equation I used to find the velocity of the particles. This gives an equation that I'm pretty sure cannot be solved and does not make much sense.

 

[Redbelly98]

Ugghhhhh.

I don't get it. The two particles have different masses but yet I have to solve for a single potential difference.

I don't have an actual r value all I have is the difference. So I have to sub back into the equation I used to find the velocity of the particles. This gives an equation that I'm pretty sure cannot be solved and does not make much sense.

If you show what equation you get, I can tell you if it's right, wrong, or can or cannot be solved.

 

[Jimmy25]

I tried to use latex but it got a little to crazy for me. A photo of my work is attached.

The solution I get for voltage I get is huge. I think something is wrong.

(I converted amu to kg for the masses of the particles and used e for the charges)

 

[Redbelly98]

That's pretty good, you're almost there, just a couple of problems to iron out:

1. Watch the units, the separation is not 1.1 meters.

2. The separation of the two charges is not simply equal to the difference in radii. Try drawing a picture; the two charges start from the same point and each travels 1/2 of a circle. What is their separation, in terms of radius or diameter, after going 1/2 way around the circle?

You nearly have it.

 

[Jimmy25]

I still get a rather large number (9.11*10⁴ V). Is this what I should expect?

 

[Jimmy25]

9.22*10⁴ V is not correct.

Everything looks good to me. Although I still don't see how the same potential difference can accelerate two particles of different masses to the same speed.

I am supposed to give my answer in MV so a large number is expected.

 

[Jimmy25]

I got it! I went through the calculation again and found another minor error and everything worked out.

Thanks!

 

[Redbelly98]

You're welcome, glad it worked out.