Solving for Radius in Magnetic Field: q of Sr+?

• wjdgone
In summary, the Lorentz Force can be applied to sort ions based on their charge to mass ratio, such as in separating isotopes or as a mass spectrometer. The problem involves a beam of Strontium ions accelerated through a 500 V potential and injected into a 1 T magnetic field. The atomic mass of Strontium is given as 87 AMU and the task is to find the value of R in cm. Using the equations r = mv/qB and E = qV = (1/2)mv^2, the value of v was first solved for and then substituted into the first equation to get r = (2mV/qB)^1/2. However, it was then realized that
wjdgone

Homework Statement

The Lorentz Force can be used to sort ions (atomic or molecular) based on their charge to mass ratio. This configuration has been used to separate isotopes and as a mass spectrometer. A beam of Strontium ions Sr+ is accelerated through a potential of 500 V and injected into a region of uniform 1 T magnetic field pointed out of the page. Strontium has an atomic mass of approximately 87 AMU (AMU = 1.66 10−27 kg ). Find R in cm.

Homework Equations

r = mv/qB (vector arrows where necessary)
E = qV = (1/2)mv^2

The Attempt at a Solution

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I solved for v with the second equation and plugged that value in the first equation and got r = (2mV/qB)^1/2, which I'm fairly certain that I'm supposed to get. What I don't get is how to solve for q (nor could I find a value online). Everything else is given; is there an equation I'm missing or something? Is q=e because Sr+ has one less electron? It's been a long time since I've done chemistry haha..

wjdgone said:
got r = (2mV/qB)^1/2
This isn't quite right. Check your derivation.

Is q=e because Sr+ has one less electron?
Yes.

TSny said:
This isn't quite right. Check your derivation.

Ah, I see. Thanks for your help.

1. What is the equation for solving for the radius of a Sr+ ion in a magnetic field?

The equation for solving for the radius of a Sr+ ion in a magnetic field is r = qB/mv, where r is the radius, q is the charge of the ion, B is the magnetic field strength, m is the mass of the ion, and v is the velocity of the ion.

2. How do I determine the charge of a Sr+ ion in a magnetic field?

The charge of a Sr+ ion can be determined by looking at its atomic structure. Since Sr+ has one less electron than Sr, it has a positive charge of +1. This charge can also be confirmed by using a mass spectrometer to measure the mass-to-charge ratio of the ion.

3. Can the radius of a Sr+ ion in a magnetic field be negative?

No, the radius of a Sr+ ion in a magnetic field cannot be negative. The equation r = qB/mv only gives positive values for the radius.

4. What units should be used for the variables in the equation for solving for the radius of a Sr+ ion in a magnetic field?

The magnetic field strength (B) should be in units of tesla (T) or gauss (G), the charge (q) should be in units of coulombs (C), the mass (m) should be in units of kilograms (kg), and the velocity (v) should be in units of meters per second (m/s).

5. Can this equation be used for other ions or only for Sr+ ions?

This equation can be used for any ion, as long as the mass and charge of the ion are known. It can also be used for charged particles other than ions, such as electrons or protons, as long as their mass and charge are known.

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