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.

Their idea was based on simulation of hypothetical conditions in the lab trying to achieve exactly similar experimental scenario on the early Earth as to test the biochemical origins of life.

Urey and Miller were testing the hypothesis of Alexander Oparin’s and J.B.S Haldane’s hypothesis, as they said that “conditions on the primitive earth favored chemical reactions that synthesized organic compounds from inorganic precursors.” This is consider to be classical experiment on the origin of life.
The reason that this experiment is consider a significant since after Miller’s death in 2007, scientists examined sealed vials preserved from the original experiments. They were able to show that there were well over 20 different amino acids produced in Miller’s original experiments. That is considerably more than those Miller originally reported, and more than the 20 that naturally occur in life.
Possibly one of the most important experiments was one conducted in 1952, when the scientists Urey and Miller, who were interested in the origin of life, and they carried out an experiment, to simulate an early Earth atmosphere. And you can see this rather ingenious apparatus where they’ve got some water boiling away inside a flask, being circulated into another container that’s got an electrical discharge apparatus. And this electrical discharge is discharging across an ancient simulated Earth atmosphere.
And they circulated this water round and round. And after a period of time, they found that the gases in this container, once they had been electrically sparked, transform themselves into amino acids, that we saw, are the building blocks of life. So, in this simple experiment, using only water and the constituents of early Earth atmosphere, these scientists managed to create the building blocks of life. This was a truly remarkable experiment, a breakthrough in astrobiology that allowed scientists to go from speculation about the origin of life, to thinking about how those early building blocks might well have formed. Nowadays we think that the atmosphere of early Earth is actually slightly different from the atmosphere that was used by Urey and Miller in the early experiments. But nevertheless this remains a remarkable and landmark experiment in the early history of Astrobiology, at least in the twentieth century. And taking our understanding of the origin of life to a new, empirical level.
References
[1] Hill H.G. & Nuth J.A. (2003). “The catalytic potential of cosmic dust: implications for prebiotic chemistry in the solar nebula and other protoplanetary systems”. Astrobiology 3 (2): 291–304. doi:10.1089/153110703769016389. PMID 14577878.
[2] Balm S.P; Hare J.P. & Kroto H.W. (1991). “The analysis of comet mass spectrometric data”. Space Science Reviews 56: 185–9. doi:10.1007/BF00178408.
[3] Miller, Stanley L. (1953). “Production of amino acids under possible primitive Earth conditions” (PDF). Science 117 (3046): 528. doi:10.1126/science.117.3046.528. PMID 13056598.
[4] Miller, Stanley L.; Harold C. Urey (1959). “Organic ccompound synthesis on the primitive Earth”. Science 130 (3370): 245. doi:10.1126/science.130.3370.245. PMID 13668555. Miller states that he made “A more complete analysis of the products” in the 1953 experiment, listing additional results.
[5] A. Lazcano, J.L. Bada (2004). “The 1953 Stanley L. Miller experiment: fifty years of prebiotic organic chemistry”. Origins of Life and Evolution of Biospheres 33 (3): 235–242. doi:10.1023/A:1024807125069. PMID 14515862.
[6] Bada, Jeffrey L. (2000). “Stanley Miller’s 70th Birthday”. Origins of life and evolution of the biosphere (Netherlands: Kluwer) 30: 107–12.
[7] BBC: The spark of life. TV documentary, BBC 4, 26 August 2009.
[8] “Right-handed amino acids were left behind”. New Scientist (2554). Reed Business Information Ltd. 2006-06-02. p. 18. Retrieved 2008-07-09.
[9] Brooks D.J. et al (2002). “Evolution of amino acid frequencies in proteins over deep time: inferred order of introduction of amino acids into the genetic code”. Molecular Biology and Evolution 19 (10): 1645–55. PMID 12270892