The Discovery of the Electron (AQA A Level Physics)

In an experiment to measure the charge of the electron, a spherical charged oil droplet of unknown mass is observed between two horizontal parallel metal plates, as shown in Figure 1.

Figure 1

The droplet falls vertically at its terminal speed when the potential difference (pd) between the plates is zero. A droplet of radius r falls at its terminal velocity, v.

Derive an expression for r in terms of v, η , ρ and g, where η is the viscosity of air and ρ is the density of the oil droplet.

Explain how the mass of the oil droplet can be calculated from its radius and other relevant data.

A potential difference (pd) is applied across the plates and is adjusted until the droplet is held stationary.

The two horizontal parallel metal plates are 15.0 mm apart. The mass of the droplet is 3.4 × 10⁻¹⁵ kg. The droplet is held stationary when the pd across the plates is 1560 V.

Calculate the charge of the oil droplet.

Give your answer in coulombs.

A student carries out Millikan’s oil drop experiment and obtains the following results for the charges on the oil drops that were investigated.

Discuss the extent to which the student’s results support Millikan’s conclusion and how the student’s conclusion should be different.

Figure 1 shows apparatus which can be used to determine the specific charge of an electron.

Figure 1

Electrons are emitted from the filament and accelerated by a potential difference between the filament and anode to produce a beam. The beam is deflected into a circular path by applying a magnetic field perpendicular to the plane of the diagram.

Describe the process that releases the electrons emitted at the filament.

Table 1 shows the data collected when determining the specific charge of the electron by the method shown in Figure 1.

Table 1

Show that the specific charge of the electron is given by the expression .

Using data from Table 1, calculate a value for the specific charge of the electron.

Give your answer to an appropriate number of significant figures.

Give your answer in coulombs per kilogram.

At the time when Thomson measured the specific charge of the particles in cathode rays, the largest specific charge known was that of the hydrogen ion.

State how Thomson’s result for the specific charge of each particle within a cathode ray compared with that for the hydrogen ion and explain what he concluded about the nature of the particles.

Figure 1 shows an experiment to measure the charge of the electron.

Figure 1

Negatively charged oil droplets are sprayed from the atomiser into the gap between the two horizontal metal plates. A potential difference is applied between the metal plates.

One of the droplets remains stationary.

Identify the forces acting on the stationary droplet. In your answer you should state the relationship between the forces.

The upthrust on the droplet due to the air it displaces is negligible.

The potential difference between the plates is changed to zero and the droplet falls at a terminal velocity of 1.0 × 10⁻⁴ m s ⁻¹ .

The density of the oil is 880 kg m⁻³

The viscosity of air is 1.8 × 10⁻⁵ N s m⁻²

Show that the radius of the droplet is about 1 × 10⁻⁶ m.

Assume that the droplet is spherical.

The potential difference between the plates is restored to its initial value and the droplet becomes stationary.

The charge on the droplet is −4.8 × 10⁻¹⁹ C.

A student suggests that, if the droplet splits into two spheres of equal size, both spheres would remain stationary.

Deduce whether this suggestion is correct.

Robert Millikan experimented with oil drops to determine a value for the electronic charge.

Figure 4 shows a stationary oil droplet between two horizontal metal plates. The plates are connected to a variable voltage supply so that the upper plate is positive. The oil droplet has mass and charge .

Figure 4

State and explain the sign of the charge on the oil droplet.

The variable voltage supply is set to zero volts. The oil drop falls. The constant speed of the falling oil droplet is found to be 3.8 × 10⁻⁵ m s⁻¹ and the following measurements are recorded:

density of oil = 910 kg m⁻³
viscosity of air = 1.8 × 10⁻⁵ N s m⁻²

Show that the mass of the oil droplet is about 8 × 10⁻¹⁶ kg.

The variable voltage supply is adjusted so that the oil droplet rises at a constant speed . The potential difference (pd) across the plates is and the distance between the plates is .

In his experiment, Millikan measured the constant speed of a falling droplet when the pd was zero. He compared this with the speed of the same droplet when the droplet was made to rise.

Show that .

The following measurements are made for the droplet in part (b) when it is rising at constant speed.

= 715 V

= 1.1 × 10⁻⁴ m s⁻¹

The separation of the plates = 11.6 mm.

Deduce, using the equation in part (c), whether the value of the charge for this droplet is consistent with the currently accepted value of the electronic charge.

After Millikan published his results, it was found that he had used a value for the viscosity of air that was smaller than the actual value.

Discuss the effect this error had on Millikan’s value of the electronic charge.