Investigating the Absorption of Radiation in Matter using G-M Counter

Figure 1: elements of Millikan Oil Drop Experiment 

 Abstract

In this experiment we will calculate the value of the electron. Using the electric field, Millikan chamber, telescope and some other tools. The elementary charge of electron is measured and found to be:

Q = 1 x 10^-19 c

Our result is in acceptable agreement with the real value, namely:

Q =1.6 *10^-19 c

Introduction

After Thomson’s measurement of e/m and the confirmation of the cathode ray as a charge carrier (called electron), several investigators attempted to determine the actual magnitude of the electron’s charge. In 1911 the American physicist Robert A. Millikan (1868– 1953) reported convincing evidence for an accurate determination of the electron’s charge. Millikan’s classic experiment began in 1909 at the University of Chicago. The experiment consisted of visual observation of the motion of uncharged and both positively and negatively charged oil drops moving under the influence of electrical and gravitational forces. The essential parts of the apparatus are shown in Figure 2. As the drops emerge from the nozzle, frictional forces sometimes cause them to be charged. Millikan’s method consisted of balancing the upward force of the electric field between the plates against the downward force of the gravitational field. _[1][2]

Figure 2: (a) Diagram of the Millikan oil-drop experiment to measure the charge of the

electron.Some of the oil drops from the atomizer emerge charged, and the electric field (voltage)

is varied to slow down or reverse the direction of the oil drops, which can have positive or negative

charges. (b) A student looking through the microscope is adjusting the voltage between the plates

to slow down a tiny plastic ball that serves as the oil drop.

There are several forces acting on the droplet and the result of these forces depends on the type of charge the droplet carries, so if the drop is negatively charged, the electric force will be up and the weight is down and a retarding force opposite of the direction of motion as shown in the figure 3.b.

We can calculate the weight of the drop through the equation of motion by observing the movement of the drop as it falls with a telescope. While watching the movement of drops through the telescope, we will find that there are drops that will rise to the top, and the reason is that the electrical force is greater than the weight. Some of them go down and the reason is that the weight is greater than the electric force, and some are at rest due to the equal weight of the electric force as shown in the figure 3.a.

Figure 3: (a) forces acting on the droplet as it falls down with no field applied, and (b)

forces acting on the droplet as it rises under the influence of the applied electric field

When an oil drop falls downward through the air, it experiences a frictional force f proportional to its velocity due to the air’s viscosity as shown in equation 12.

This force has a minus sign because a drag force always opposes the velocity. The constant b is determined by Stokes’s law and is proportional to the oil drop’s radius. Millikan showed that Stokes’s law for the motion of a small sphere through a resisting medium was incorrect for small-diameter spheres because of the atomic nature of the medium, and he found the appropriate correction. The buoyancy of the air produces an upward force on the drop, but we can neglect this effect when the drop is at rest. _[1]

In order to calculate the weight, we turn off the electric field and the drop falls freely, but the retarding force (stoke’s force) of the air reduces the velocity of the drop towards the bottom until it finally reaches a constant speed called (terminal velocity) and then we calculate the weight from the equations of motion and the value of the electric field is known and thus the charge of the drop becomes known .

But an oil drop does not contain just one electron, but rather many electrons.

Millikan used x-rays to ionize the air inside the cylinder, so the droplet would acquire a number of charges.

Millikan found that the difference sources in the charge always give a constant value, which is (e). Therefore, Millikan concluded that this number is the lowest charge that the drop can carry, which is the same as the charge of the electron.

 

Formalism

Equations of the Null Method:

Equations of the Kinetic Method

Read alsoKerr Effect Experiment

Read alsoGamma Ray Spectroscopy

Read alsoElectron Spin Resonance

Read alsoInvestigating the Absorption of Radiation in Matter using G-M Counter

Experimental Methods

In this experiment we use the electric field to calculate the charge of electron.

As shown in the Figure 1, there is an atomizer that sprays oil droplets inside a cylinder (chamber). Inside the cylinder, there are two rounded plates, one of which is positively charged and the other negative, which results in a regular electric field. When the charged droplet enters an electric field, it is affected by an electric force. We can observe the droplets by a telescope. There are also a scale it used to know the distance that the droplet travel. There are a power supply to make the voltage.

In this experiment we will use the kinetic meth, so the steps will be as the following:

-We atomize the oil into the chamber by squeezing the rubber bulb. And we focus on the oil droplets.

- The droplets fall under the influence of gravity.

- We focus on one drop and switch the timer, when the drop travels a full scale we turn off the timer.

-We keep the reading of the timer (T₁).

-We raise the voltage to the tope around (576), the droplets start to move upward.

- We focus on one drop and switch the timer, when the drop travels a full scale, we turn off the timer.

- We keep the reading of the timer (T₂).

-We repeat the previous steps 12 times and every time we change the oil drop.

-We record the result in a table.

- Then we calculate the speed of each drop V₁ and V₂.

-We calculate the electron charge in each drop.

-Divide each charge on the smallest charge.

-Multiply Q/Q_s by the factor to get the best integers.

- Represent the relationship between N and Q in the graph and calculate the slope.

Data Analysis 

Slope = 1x 10^^-19

Figure 3: charge in each droplet Q against to the corresponding integer

Conclusion

Millikan made thousands of measurements using different oils and showed that there is a basic quantized electron charge. Millikan’s value of e was very close to our presently accepted value of ( ) Notice that we always quote a positive number for the charge e. The charge on an electron is then – e.

References

1-Modern Physics for Scientists and Engineers Fourth Edition Stephen T. Thornton.

2-EXPERIMENTS In MODERN PHYSICS Second Edition Adrian C. Melissinos Jim Napolitano