Once Rutherford and Geiger determined the charge-tomass...

Once Rutherford and Geiger determined the charge-tomass ratio of the alpha particle (Problem 81 ), they performed another experiment to determine its charge. An alpha source was placed in an evacuated chamber with a fluorescent screen. Through a glass window in the chamber, they could see a flash on the screen every time an alpha particle hit it. They used a magnetic field to deflect beta particles away from the screen so they were sure that every flash represented an alpha particle. (a) Why is the deflection of a beta particle in a magnetic field much larger than the deflection of an alpha particle moving at the same speed? (b) By counting the flashes, they could determine the number of alphas per second striking the screen $(R)$. Then they replaced the screen with a metal plate connected to an electroscope and measured the charge $Q$ accumulated in a time $\Delta t$. What is the alpha-particle charge in terms of $R, Q$, and $\Delta t ?$

Once Rutherford and Geiger determined the charge-tomass ratio of the alpha particle (Problem 81 ), they performed another experiment to determine its charge. An alpha source was placed in an evacuated chamber with a fluorescent screen. Through a glass window in the chamber, they could see a flash on the screen every time an alpha particle hit it. They used a magnetic field to deflect beta particles away from the screen so they were sure that every flash represented an alpha particle.
(a) Why is the deflection of a beta particle in a magnetic field much larger than the deflection of an alpha particle moving at the same speed? (b) By counting the flashes, they could determine the number of alphas per second striking the screen $(R)$. Then they replaced the screen with a metal plate connected to an electroscope and measured the charge $Q$ accumulated in a time $\Delta t$. What is the alpha-particle charge in terms of $R, Q$, and $\Delta t ?$

Key Concepts

Determining Charge via Particle Counting

One method to determine the charge on individual particles involves measuring the total charge accumulated over a given time interval while simultaneously counting the number of particles arriving in that period. By using the relationship Q = (number of particles) × (charge per particle), where the number of particles is determined by the rate R multiplied by the time interval ?t, one can calculate the charge per particle as q = Q/(R?t).

Magnetic Deflection of Charged Particles

Charged particles moving in a magnetic field experience a Lorentz force that is perpendicular to both their velocity and the magnetic field. This force causes them to follow a curved (often circular) path. The radius of this curvature is given by the expression r = mv/(qB), which implies that for particles with the same speed and magnetic field strength, a smaller mass or a larger charge results in a tighter curvature. Thus, lighter particles such as beta particles (electrons) are deflected more than heavier particles like alpha particles.

Charge-to-Mass Ratio

The charge-to-mass ratio (q/m) is a crucial parameter in understanding the behavior of charged particles in magnetic and electric fields. It directly influences the force experienced by the particle and therefore the degree of deflection observed in a magnetic field. Since beta particles have a much smaller mass compared to alpha particles (even though the charge magnitude may be similar), their higher q/m ratio leads to a larger deflection under the same conditions.

Transcript

00:01 So this question is actually a continuation of the previous question, talking about the alpha particles being emitted by uranium 235.

00:13 I'm trying to find out what is the charge and mass of these particles.

00:19 That's being emitted.

00:21 Back then, alpha particles were still unknown, so they don't know what is the charge and mass.

00:26 And they're carrying out these experiments to find out what exactly is the charge and the mass.

00:31 So for this part of the experiment we didn't know the charge to mass ratio and we're trying to determine what is the exact charge.

00:42 So the first part we are looking at a process of eliminating beta particles from the stream of alpha and beta particles.

00:54 So there's this stream where there is like alphas and there's also beta.

00:59 But we want to deflect them away.

01:01 And they do that by applying a magnetic field and i try to figure out why this magnetic field reflects beta much more than the alpha all right so first we assume assume that the speed of these alpha particles is the same as the beta particles right since we have a velocity selector which we can select a specific velocity of the charge particles and then subsequently we know what is the force that the magnetic field would apply on these particles and the force is equals to qvb alright so the force applied on an alpha particle would be equals to q charge of alpha particle plus velocity times b right the force of the beta particle is q terms beta, v alpha, i mean v beta, right, but v beta is actually the same as v alpha, right? we assume that they are the same.

02:27 And now you know that the charge, right, of the alpha particles is actually twice, twice that of the charge of beta particles.

02:43 Right, the absolute value.

02:47 Of alpha particles charge is actually twice the absolute value of the charge of beta particles.

02:58 And so, if you were to look at the magnitude of the force, the magnitude of the force of alpha, actually be twice that of the force centered on the beta particles.

03:30 So now, we want to look at what is the resulting acceleration on the particles right and to look at the acceleration we know that f equals to m a so f of beta goes to mass of beta but by the acceleration of beta we know that f beta is actually half of the force of on the alpha right this is actually equal to how mass of the alpha particles times the acceleration of the alpha particles.

04:36 So right now we are just actually interested in the magnitudes, right? now magnitude of the beta acceleration then be mass of beta times half.

05:01 Okay, i hope you're following...

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