Quantization of Charge — Revision Notes

⚡ 30-Second Revision

Quantization of Charge: — Electric charge exists in discrete packets.
Formula: — $Q = \pm \ne$
Elementary Charge ($e$): — Smallest free charge unit.
Value of $e$: — $1.602 \times 10^{-19},\text{C}$ (approx. $1.6 \times 10^{-19},\text{C}$)
$n$: — Positive integer (number of elementary charges).
Electron charge: — $-e$
Proton charge: — $+e$
Experimental Proof: — Millikan's Oil Drop Experiment.

2-Minute Revision

Quantization of charge is a fundamental principle stating that electric charge is not continuous but exists in discrete, indivisible units. This means any observable charge $Q$ is always an integer multiple of a basic unit called the elementary charge, '$e$'.

The formula is $Q = \pm \ne$, where $n$ is a positive integer ($1, 2, 3, \dots$) representing the number of elementary charges. The value of $e$ is approximately $1.602 \times 10^{-19},\text{C}$. Electrons carry a charge of $-e$, and protons carry $+e$.

This principle was conclusively demonstrated by Millikan's oil drop experiment. While quarks have fractional charges, they are always confined, so $e$ remains the smallest free unit of charge. Macroscopically, charge appears continuous because the number of elementary charges involved is astronomically large.

Remember to differentiate this from the conservation of charge, which states that total charge in an isolated system remains constant.

5-Minute Revision

The concept of quantization of charge is pivotal in understanding electricity. It posits that electric charge is not infinitely divisible but comes in fixed, fundamental 'packets' or 'quanta'. The smallest such packet for a free particle is the elementary charge, denoted by '$e$', with a value of approximately $1.

602 \times 10^{-19},\text{C}$. This means any total charge$Q$on an object must be an integer multiple of$e$, expressed as$Q = \pm \ne$. Here,$n$ is a positive integer, indicating the number of elementary charges gained or lost.

For instance, if an object loses $10^{10}$ electrons, its charge becomes $Q = +(10^{10}) \times (1.6 \times 10^{-19},\text{C}) = 1.6 \times 10^{-9},\text{C}$. Conversely, if an object has a charge of $-3.

2 \times 10^{-18},\text{C}$, the number of excess electrons is$n = \frac{|-3.2 \times 10^{-18},\text{C}|}{1.6 \times 10^{-19},\text{C}} = 20$. The experimental validation for this principle came from Millikan's oil drop experiment, which showed that all measured charges were discrete multiples of$e$.

It's important to note that while quarks have fractional charges, they are never found in isolation, thus $e$ remains the smallest free charge. At the macroscopic level, charge appears continuous because the number of elementary charges involved is typically enormous, making the discrete nature imperceptible.

Always ensure $n$ is an integer when solving problems related to possible charges.

Prelims Revision Notes

1
Definition: — Electric charge is quantized, meaning it exists only in discrete, integral multiples of a fundamental unit of charge.
2
Elementary Charge ($e$): — The smallest magnitude of charge found on a free particle. It is the charge of a proton ($+e$) or an electron ($-e$).
3
Value of $e$: — $e \approx 1.602 \times 10^{-19},\text{Coulombs (C)}$. For NEET calculations, $1.6 \times 10^{-19},\text{C}$ is commonly used.
4
Quantization Formula: — $Q = \pm \ne$

* $Q$: Total charge on an object. * $n$: A positive integer ($1, 2, 3, \dots$), representing the number of elementary charges. * $\pm$: Indicates excess (negative) or deficit (positive) of electrons.

1
Implications:

Charge cannot be arbitrarily divided; there's a minimum unit. If a calculated $n$ is not an integer, that charge value is not possible for a free particle.

1
Experimental Proof: — Millikan's Oil Drop Experiment (1909) conclusively demonstrated charge quantization by showing all measured charges were integral multiples of $e$.
2
Quarks: — Fundamental particles with fractional charges ($\pm \frac{1}{3}e, \pm \frac{2}{3}e$). However, they are always confined within hadrons (like protons and neutrons), so they are not observed as free particles. Thus, $e$ remains the smallest free charge.
3
Macroscopic vs. Microscopic: — At the microscopic level, charge is discrete. At the macroscopic level, due to the extremely large number of elementary charges involved, charge appears continuous.
4
Distinction from Conservation of Charge:

* Quantization: Deals with the nature (discrete units) of charge. * Conservation: Deals with the persistence (total charge constant in isolated system) of charge.

1
Common Calculations:

* Given $Q$, find $n$: $n = |Q|/e$. * Given $n$, find $Q$: $Q = \pm \ne$. * Example: $1\,\text{C}$ of charge corresponds to $n = \frac{1}{1.6 \times 10^{-19}} \approx 6.25 \times 10^{18}$ elementary charges.

Vyyuha Quick Recall

Q = ne: 'Q'uantum 'N'umber 'E'lementary. Remember, 'Q' is always a 'N'ice, 'E'ven number of 'e's!