Physicist S. A. Goudsmit devised a method for measuring the mass of heavy ions by timing their p

Physicist S. A. Goudsmit devised a method for measuring the...

Key Concepts

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in a magnetic field, expressed as F = qvB. This force acts perpendicular to both the direction of motion and the magnetic field, causing the particle to move in a circular path when velocity and magnetic field are perpendicular.

Circular Motion in a Magnetic Field

When a charged particle moves perpendicular to a uniform magnetic field, the magnetic force becomes a centripetal force, causing the particle to undergo uniform circular motion. The balance of the magnetic and centripetal forces provides a relationship between the particle's speed, mass, and the radius of its circular path.

Cyclotron Frequency

Cyclotron frequency is the frequency with which a charged particle orbits in a magnetic field, given by the formula f = qB/(2?m). It is a key parameter in devices like cyclotrons and is used to determine the mass-to-charge ratio of ions based on their revolution period.

Mass Determination Using Revolution Period

The mass of a charged particle can be determined by measuring the time it takes to complete a known number of revolutions in a magnetic field. By relating the measured period to the cyclotron frequency and using the balance between magnetic and centripetal forces, one can extract the particle's mass.

Unit Conversion

Accurate physical calculations often require converting units, such as transforming magnetic field values from milliTesla to Tesla, time from milliseconds to seconds, or mass from kilograms to atomic mass units. Proper unit conversion is essential for ensuring the consistency and comparability of computed physical quantities.

Transcript

00:01 Okay, folks, so in this video we're going to be talking about this problem.

00:05 Physicist s .a.

00:07 I'm sorry, i can't pronounce this name.

00:09 This guy devised a method for measuring the mass of heavy ions by timing their period of revolution in a known magnetic field.

00:19 So a singly charged ion of iodine makes seven revolutions in a 45mt field in 1 .29 milliseconds.

00:31 Calculate its mass in atomic mass units.

00:37 Okay, so this problem is not necessarily, conceptually speaking, difficult to understand.

00:48 So before we get started doing it, let's just see if we can conceptually understand it, because i think that's the most important thing.

01:00 If you have, you know, a charged particle moving in a magnetic field, it's going to be deflected.

01:09 It's going to be swirling around.

01:12 So, for example, if your b field, you know, your magnetic field points into the page, right? and then you have a either positively charged or a negatively charged particle moving in this region.

01:28 No, this is your particle.

01:30 It's not just going to move straight in a straight line, right? if it doesn't, if it's already moving with a velocity in vacuum, then it's going to keep moving in a straight line.

01:43 But since this is not a vacuum, this is a, it's not moving in a vacuum.

01:49 It's moving in a magnetic field.

01:51 What it's going to do is that it's not going to keep its straight, you know, straight path.

01:55 It's going to start whirling around in a circular motion.

02:00 Right? so we can find out a lot about this particle, given the fact that it's moving in a circular motion.

02:10 So here's what i mean by that.

02:12 We know from newton's second law that mass times acceleration equals the force, right? what is the acceleration of a particle that is moving circularly? it is v squared over r.

02:28 Now, on the other hand, what is the force on this particle.

02:33 It is the magnetic, magnetic force, right? so it depends on q.

02:38 It also depends on v -cross -b, but we're just going to assume that v and b are perpendicular, because that's how you make the particle whirl around.

02:49 So v -cross -b is just going to give you magnitude of v times the magnitude of b with a science theta, which i'm going to ignore because they're perpendicular.

02:58 Okay.

02:59 So let's simplify this.

03:01 V and v squared, you can cross out one of the vs.

03:05 So you're left with m v over r equals qb.

03:10 What we're looking for is we're looking for the mass, right? what do we know? do we know the charge? well, we actually do.

03:20 Because in this problem, what we have is a single, i'm sorry, singly charged ion, right? what does the mean for a particle? for an ion to be singly charged.

03:34 It means one electron has been ripped off of it.

03:39 If that electron was not ripped off of it, then this thing wouldn't be called an ion...

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