Q. Describe in brief the discharge of electricity through a gas.

or,

[su_heading size=”17″]Q. Describe with a neat diagram of the phenomenon of electrical discharge through gases.[/su_heading]

Ans: We know that the gases are good insulators of electricity at normal pressure and temperature. But, we can make them conducting by:

• Applying very high voltage (~30,000 V/cm)
• Reducing its pressure to a very low value (~ 0.01 mm of Hg)

By imposing the above conditions to the gases, they split into the charged particles, called ions, both positive and negative and hence the electric current flows through them which is known as electrical conduction or discharge in the gas. We use the glass tube to study the electrical conduction through gases at low pressure called the discharge tube. This experiment was conducted initially by Sir William Crookes, Thomson, and many others.

Experimental set-up:

The experimental set-up consists of a strong glass tube of about 0.5 m long and 0.0 m in diameters, closed at both ends and provided with two platinum electrodes A and C, called anode and cathode respectively. These two electrodes are connected to the secondary terminals of a powerful induction coil. The discharge tube is connected with a vacuum pump to reduce the pressure inside the tube and pressure gauge to measure the pressure inside the tube as shown in the figure below.

                                     Fig: Discharge of electricity through gases at low pressure.

As the pressure inside the discharge tube is gradually decreased with the help of pressure gauge, the following phenomena are observed as discussed below:

(i) At a pressure about 10 mm of Hg:

When the pressure in the discharge tube is reduced to about 10 mm of Hg, the discharge occurs in the tube showing luminous streaks between the electrodes A and C, these streaks are called blue streamers which are produced with cracking noise.

(ii) At a pressure about 5 mm of Hg:

At this pressure inside the tube, the blue streaks broaden out in a luminous column which is bright and steady and this column is called Geissler’s discharge. The color of the discharge depends on the nature of the gas.

(iii) At a pressure of 2 mm of Hg:

In this case, a long luminous column appears from A to C inside the tube and this column is called the positive column. Again, the color of the discharge depends on the nature of the gas. For eg: blue for hydrogen and red for air.

(iv) At a pressure of 1 mm of Hg:

When the pressure inside the tube is reduced to 1 mm of Hg, the positive column leaves the cathode and moves to the anode. A blue luminous glow appears at a cathode called a negative glow. A dark space appears between the positive column and negative glow which is called Faraday’s dark space as shown below;

(v) At a pressure of 0.5 mm of Hg:

As the pressure inside the discharge tube is further reduced to about 0.5 mm of Hg, the size of the positive column gets reduced whereas the  Faraday’s dark space extends to a longer size. The negative glow leaves the cathode and another glow appears on the cathode called cathode glow. The negative glow moves towards the anode. Also, another dark space appears between cathode glow and negative glow which is known as Crooke’s dark space.

(vi) At a pressure of 0.05 mm of Hg: 

In this range of pressure, the positive column further shortens and breaks into an alternative bright and dark disc called striations as shown below;

(vii) At a pressure of about 0.01 mm of Hg: 

In this reduced pressure inside the discharge tube, initially, the striations disappear, and then negative and cathode glow vanishes. Then the whole tube is filled with Crooke’s dark space. At this situation, the luminous rays are seen to come out of the cathode which are called cathode rays.

In this way, the cathode rays are produced. If the pressure in the tube is reduced further, the tube stops conducting.

[su_heading size=”17″]Cathode rays: [/su_heading]

What are the cathode rays? write its properties. [imp: 2 marks]

Ans: Cathode rays are the invisible rays emerging normally from the cathode of a discharge tube, kept at a pressure of 0.01 mm of Hg, and under a very high potential difference of the order of several thousand volts (10-15 KV). These rays are independent of the nature of gas and their propagation is independent of the position of the anode.

Properties of cathode rays:

1. Cathode rays are emitted normally from the surface of the cathode.
2. Cathode rays can penetrate the small thickness of matter such as sheets of aluminum foil.
3. They can travel in a straight line and cast sharp shadows of the targets placed in their path.
4. They carry negative charge so are deflected by electric and magnetic fields.
5. They carry momentum and kinetic energy.
6. They produce heat when they fall upon the matter.

Reference: Principle of physics, Ayam publication.

Electron is a negatively charged ordinary particle found in all types of matter. The term “electron” was first suggested by Stoney in 1891, although the electron was not discovered until 1897 by British physicist J.J. Thomson. Each electron carries one unit of negative charge (1.602 x 10^-19 coulomb) and has a tiny mass compared to a neutron or proton. The mass of an electron is 9.10938 x 10^-31 kg. This is about 1/1836 the mass of a proton. A common symbol for an electron is e^–.

The electron’s antiparticle, which carries a positive electric charge, is called a positron or antielectron. A positron is denoted using the symbol e⁺ or β⁺.

Properties of the electron:

• Electrons are negatively charged tiny particles.
• The mass of an electron is 9.10938 x 10^-31 kg. This is about 1/1836 the mass of a proton.
• They show both particle-like and wave-like behaviour.
• Quantum mechanical properties of electrons include an intrinsic angular momentum spin of the value of half of reduced Planck's constant.

Millikan’s oil drop experiment

[su_heading]Q. Describe the necessary theory and calculations of Millikan’s oil drop experiment for the measurement of the charge of an electron [4].[/su_heading]

The experimental arrangement of Millikan’s oil drop experiment consists of two circular metal plates of about 20cm in diameter and 1.5 cm of separation with a small hole in the centre of the upper plate through which a drop of non-volatile oil is sprayed with the help of an atomizer. These oil drops get charged due to friction and get ionized due to the X-ray provided through window W₁ Also, window W₂ is open to provide enough light to illuminate the oil drop, as shown in the figure below. These two parallel horizontal plates are connected to two terminals of the H.T battery to provide electric field E, as given below in the figure.

                                      [a]                                                        [b]                                   [c]

                                            Fig: Experimental set-up.                                                          Effect of gravity alone.               Gravity+ electric field.

The experiment is done in the following two steps:

1. The motion of oil drop in the absence of an electric field  [Motion of drop under gravity alone].

In this case, the oil drop falls under the action of gravity alone, reaching a constant velocity called terminal velocity when the viscous force becomes equal to its resultant weight. At terminal velocity, the net force acting on the drop must be zero.

Net Force = 0

   i.e, Upthrust + Viscous force = Weight  [fig ‘a’]

U + F = W

Assuming oil drop spherical, Upthrust (U) = volume of air displaced x density of air x acceleration due to gravity.

[latex] U= \frac {4}{3} \pi r^3 \sigma g  [/latex]

Now, From Stoke’s law, Viscous force is given by;

[latex] (F)= 6 \pi \eta r v_1 [/latex]

Also, we know, The volume of oil drop = Volume of air displaced.

[latex] So\; Weight \; of\; oil\; drop\; (W)=\frac {4}{3} \pi r^3 \rho g [/latex]

Where $ \rho $ is the density of an oil.

Hence, the above equation becomes,

[latex]\frac {4}{3} \pi r^3 \sigma g + 6 \pi \eta r v_1= \frac {4}{3} \pi r^3 \rho g [/latex]

or, [latex] 6 \pi \eta r v_1 = \frac {4}{3} \pi r^3 (\sigma – \rho) g\\ [/latex]

[latex] \therefore r= \sqrt{\frac{9}{2} \frac{\eta v_1} {(\rho -\sigma) g}}[/latex]

This equation gives the radius of the oil drop, considering the effect of gravity alone.

2. The motion of the oil drop under the combined effect of gravity and electric field:

In this case, the experiment is conducted under the effect of gravity and the electric field (E) with total charge ‘q’ when the strength of the electric field is strong enough to cause the oil drop to move in an upward direction with velocity v₂ as shown in figure (c) above.

Then, the net force acting on an oil drop = 0.

Here, in this situation, the forces acting in an upward direction are upthrust (U) and electric field (E), whereas viscous force and the weight of the oil drop are acting in a downward direction.

i.e,  Electrostatic force + upthrust = Viscous force + Weight

[latex] or, qE+ \frac{4}{3} \pi r^3 \sigma g- 6\pi \eta r v_2- \frac{4}{3} \pi r^3 \rho g=0 \\ [/latex]

or, [latex] qE= \frac{4}{3} \pi r^3 (\rho- \sigma) g+ 6\pi \eta r v_2 \\ [/latex]

[latex] \therefore q= \frac{1}{E} \big[\frac{4}{3} \pi r^3 (\rho- \sigma) g+ 6\pi \eta r v_2\big] \\ [/latex]

So, finally ;

[latex] \therefore q= \frac{6\pi \eta \:(v_1+ v_2)\:r} {E}\\ [/latex]

Using the value of the radius of the oil drop (r), the above equation takes the following form;

[latex] q= 6\pi\eta  \frac{(v_1+v_2)}{E} \big[ \sqrt{\frac{9}{2} \frac{\eta v_1} {(\rho -\sigma) g}}\big] [/latex]

————[A]

If the oil drop moves in a downward direction even if the electric field is applied, then the above equation modifies as follows;

[latex] q= 6\pi\eta  \frac{(v_1-v_2)}{E} \big[ \sqrt{\frac{9}{2} \frac{\eta v_1} {(\rho -\sigma) g}}\big] [/latex]

————[B]

In this way, we can calculate the total charge carried by an oil drop. By performing this process in a large number of times, it is found that the value of ‘q’ is an integral multiple of a small unit of charge equivalent to a charge carried by an electron, i.e. 1.602 x 10^-19 coulomb.

This means that the total charge 'q' on the oil drop can be expressed as;

[latex] q=ne, \; \; where \; n=1,2,3,…..[/latex]

Hence, this experiment concludes that the charge on any object exists as a multiple of small units called the quantum of charge. Each quantum of charge is equivalent to 1.602 x 10^-19 C. This is called quantization of charge.

Importance of Millikan’s Experiment:

• It shows that electronic charge was the smallest possible charge on a charged particle or ion.
• It proved the quantization of charge, i.e. body can carry an integral multiple of minimum charge (e).
• It helps to estimate an electron’s mass by using the value of the specific charge of an electron.