Electrons: Exploring Their Properties and Behavior

Dive into the fascinating world of electrons, understanding their fundamental properties and how they interact with electric and magnetic fields through key experiments like Millikan's and Thomson's.

20. Electrons

Electrons are fundamental subatomic particles, carrying a negative elementary electric charge. They are constituents of atoms, orbiting the nucleus and largely determining the chemical properties of elements. Understanding electrons is crucial for comprehending electricity, magnetism, and the structure of matter.

20.1 Millikan’s Oil Drop Experiment

The Millikan oil-drop experiment, performed by Robert A. Millikan and Harvey Fletcher in 1909, was a groundbreaking experiment that measured the elementary electric charge (e) of the electron. Before this experiment, the existence of a fundamental unit of charge was hypothesized, but its value was unknown.

Experimental Setup and Principle:

  • Tiny oil droplets, produced by an atomizer, were sprayed into a chamber.
  • Some of these droplets acquired an electric charge (either positive or negative) due to friction or by picking up stray ions in the air (often ionized by X-rays).
  • The chamber had two parallel metal plates, with a variable electric field applied between them.
  • A telescope was used to observe the motion of a single charged oil drop.

The experiment involved balancing the gravitational force on an oil drop with the upward electric force. When the oil drop was suspended motionless, the forces were equal:

F_gravity = mg

F_electric = qE

Therefore, mg = qE

Where:

  • m is the mass of the oil drop (determined by its terminal velocity when the electric field was off).
  • g is the acceleration due to gravity.
  • q is the charge on the oil drop.
  • E is the electric field strength (V/d, where V is the voltage and d is the plate separation).

Results and Significance:

Millikan observed that the charges (q) on the oil drops were always integer multiples of a fundamental value. This fundamental value was determined to be approximately 1.602 x 10-19 Coulombs, which is the charge of a single electron (or a proton). This experiment provided conclusive evidence for the quantization of electric charge.

20.2 Motion of Electron Beam in Electric and Magnetic Fields

Electrons, being charged particles, experience forces when moving through electric and magnetic fields. This interaction is fundamental to many technologies, including cathode ray tubes (CRTs), mass spectrometers, and particle accelerators.

Motion in an Electric Field:

When an electron (charge -e) enters a uniform electric field (E), it experiences an electric force (F_E) given by:

F_E = qE = -eE

This force causes the electron to accelerate in a direction opposite to the electric field. If the electron enters the field perpendicular to the field lines, its path will be parabolic, similar to projectile motion under gravity.

Motion in a Magnetic Field:

When an electron moving with velocity (v) enters a uniform magnetic field (B), it experiences a magnetic force (F_B) given by the Lorentz force law:

F_B = q(v x B) = -e(v x B)

The magnitude of the force is F_B = evBsin(theta), where theta is the angle between v and B.

  • If v is parallel or anti-parallel to B (theta = 0 or 180 degrees), F_B = 0, and the electron continues in a straight line.
  • If v is perpendicular to B (theta = 90 degrees), F_B = evB (maximum force). This force is always perpendicular to both v and B, causing the electron to move in a circular path. The centripetal force is provided by the magnetic force: mv2/r = evB, where r is the radius of the circular path.
  • If v is at an arbitrary angle to B, the motion is helical (a spiral along the magnetic field lines).

20.3 Thomson’s Experiment to Determine Specific Charge of Electrons

J.J. Thomson's experiment in 1897 was pivotal in discovering the electron and measuring its charge-to-mass ratio (e/m), also known as the specific charge. This experiment demonstrated that cathode rays were composed of negatively charged particles far lighter than hydrogen atoms.

Experimental Setup and Principle:

Thomson used a cathode ray tube (CRT), which consisted of:

  • A cathode (negative electrode) and an anode (positive electrode) to generate a beam of cathode rays (electrons).
  • A pair of parallel plates to create an electric field (E).
  • A pair of coils to create a magnetic field (B) perpendicular to both the electric field and the electron beam's velocity.
  • A fluorescent screen at the end to observe the deflection of the electron beam.

Measuring the Velocity of Electrons (Velocity Selector):

Thomson first adjusted the electric and magnetic fields such that their forces on the electron beam canceled each other out, resulting in no deflection. In this condition:

F_electric = F_magnetic

eE = evB

v = E/B

By knowing E and B, the velocity (v) of the electrons could be determined.

Measuring the Specific Charge (e/m):

Once the velocity was known, Thomson turned off the magnetic field and only used the electric field (or vice versa with the magnetic field) to deflect the beam. The deflection of the beam allowed him to calculate the charge-to-mass ratio.

If only the magnetic field is present, the magnetic force provides the centripetal force for the circular path:

evB = mv2/r

e/m = v / (Br)

By substituting v = E/B, we get:

e/m = (E/B) / (Br) = E / (B2r)

Where r is the radius of the circular path, which can be determined from the geometry of the tube and the deflection on the screen.

Results and Significance:

Thomson's experiments yielded a value for e/m of approximately 1.759 x 1011 C/kg. This value was much larger than the e/m ratio for hydrogen ions (protons), indicating that the particles making up cathode rays were either much more highly charged or, more likely, much lighter than hydrogen atoms. This led to the conclusion that these particles (electrons) were fundamental components of all atoms.

Together, Millikan's and Thomson's experiments provided the two key pieces of information (e and e/m) needed to calculate the mass of a single electron: m = e / (e/m).

m = (1.602 x 10-19 C) / (1.759 x 1011 C/kg) ≈ 9.109 x 10-31 kg

This mass is incredibly small, confirming the electron as a tiny, fundamental particle.

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