Understanding Millikan’s Oil Drop Experiment and Its Impact

Millikan’s Oil Drop Experiment stands as a major breakthrough in modern physics, directly measuring the elementary charge of the electron. Conducted by Robert Millikan in 1909, this experiment not only revealed the quantization of electric charge, but also shaped our understanding of atomic structure. In this article, we'll clearly explain Millikan’s oil drop experiment, including its aim, setup, working principle, and key results, to help you master this crucial topic in physics and chemistry.

Aim of Millikan's Oil Drop Experiment

The principal goal of Millikan’s oil drop experiment was to determine the precise value of the charge carried by a single electron. This groundbreaking work settled debates about whether electric charge was continuous or existed in discrete units.

Apparatus and Construction

The apparatus used in Millikan's experiment consists of carefully designed components for generating, observing, and controlling the motion of tiny oil droplets:

• Two parallel metal plates to create a uniform electric field (see the typical Millikan’s oil drop experiment diagram in textbooks).
• A fine spray mechanism to introduce small oil droplets between the plates.
• A DC power supply to control the electric field strength.
• A microscope for visualizing the oil drops and measuring their movement.
• An X-ray source to charge the oil drops (by ionizing surrounding air molecules).

This apparatus allowed Millikan to carefully manipulate and analyze the motion of charged oil droplets under gravity and electric forces.

Theory and Working Principle

Millikan’s oil drop experiment explained the quantization of charge by studying how oil droplets behave in a controlled environment. The experiment involves balancing the gravitational force against the electric force acting on tiny, charged droplets.

Step-by-Step Process

• Oil drops are sprayed into the space between the plates, initially falling under gravity.
• As they fall, air resistance quickly brings each droplet to a steady speed, called terminal velocity, in the absence of an electric field.
• Their terminal velocity ($v_1$) is measured using:
  \( v_1 = \frac{l_1}{t_1} \)
  where \( l_1 \) is the distance travelled, and \( t_1 \) is time taken.
• An electric field is introduced by applying voltage across the plates. This electric force acts upward, opposing gravity.
• By adjusting the voltage, some charged oil drops can be made to suspend motionless (the net force is zero) or rise with a new terminal velocity ($v_2$).
• Careful timing allows measurement of $v_2$:
  \( v_2 = \frac{l_2}{t_2} \)

Main Forces Acting on Oil Drops

• Gravity (down): \( F_g = mg \)
• Buoyancy (up): due to displaced air
• Viscous Drag: described by Stokes' Law ($ F_v = 6 \pi \eta r v $) where $\eta$ is viscosity, $r$ is drop radius
• Electric Force (up): \( F_e = qE \), $E = V/d$ (V: voltage, d: plate separation)

The balancing condition (stationary drop) is:

$$ qE = mg $$

Thus, the Millikan’s oil drop experiment formula for charge $q$ is:

$$ q = \frac{mgd}{V} $$

By repeating the experiment with different drops, Millikan found that every measured charge was an integer multiple of a smallest value, confirming that charge is quantized.

Results and Significance

• The value of the elementary charge established: \( e = 1.6 \times 10^{-19} \) C.
• Demonstrated, unequivocally, that electric charge exists in discrete units.
• Laid the foundation for advancements in atomic and modern physics.
• Supported the atomic theory of matter and revolutionized our understanding of subatomic particles. For reference on the importance of constants like the electron charge, see Planck's constant.

Related Concepts to Explore

• Balanced force
• Electric charge: definition and properties
• Fluid friction and viscosity

In conclusion, Millikan’s oil drop experiment is used to find the exact charge of an electron and to prove the discrete nature of electric charge. The precise method, carefully explained here, remains a classic in physics education—often discussed in Millikan’s oil drop experiment notes for class 11 and class 12. Understanding the procedure, forces, and formula provides a foundation for further studies involving electrostatics and atomic theory. The key takeaway: the charge of the electron ($e$) is a universal constant, critical for both theoretical and practical science.