In Milikan's experiment, static electric charge on the oil drops has been obtained by shining X-rays. If the static electric charge on the oil drop is $-1.282 \times 10^{-18}\ C$, calculate the number of electrons present on it.

In Milikan's experiment, static electric charge on the oil drops has been obtained by shining X-rays. If the s

Exercises · 2.39

-1.282 \times 10^{-18}\ C

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Concept understanding — Mass of Electron

Mass of Electron: From Intuition to Precision

Imagine you're holding a tiny grain of sand. Now imagine something 18,000 times lighter than that single grain. That's roughly the scale we're dealing with when we talk about the mass of an electron.

The electron is one of the fundamental building blocks of matter — it's the particle that orbits the nucleus of every atom, carrying a negative charge. But unlike a speck of dust or a drop of water, an electron is so small that its mass is almost impossible to grasp with everyday intuition.

The Intuitive Picture

Think of an atom as a tiny solar system. The nucleus (made of protons and neutrons) is like the Sun — heavy and dense. The electrons are like planets — but here's the twist: if the nucleus were the size of a marble, the electrons would be like specks of dust whizzing around a football field. The mass of the electron is so tiny that 99.9% of an atom's mass comes from its nucleus. The electrons contribute almost nothing to the weight of the things around you.

Note

An electron's mass is about 1/1836 of a proton's mass. That means you'd need about 1836 electrons to equal the mass of a single proton.

The Precise Statement

In physics and chemistry, the mass of an electron is a fundamental constant. Its accepted value is:

m_e = 9.1093837015 \times 10^{-31} \text{ kg}

That's 0.00000000000000000000000000000091093837015 kg — a decimal with 30 zeros before the first non-zero digit.

m_e = 9.109 \times 10^{-31} \text{ kg}

For most exam problems, you'll use the rounded value $9.1 \times 10^{-31} \text{ kg}$ .

Why This Number Matters

This tiny mass has enormous consequences. Because electrons are so light, they can move easily through conductors (that's how electricity flows). Their small mass also means they behave more like waves than particles in many situations — a key idea in quantum mechanics.

In terms of energy, Einstein's famous equation $E = mc^2$ tells us that even this tiny mass corresponds to a measurable amount of energy: about $8.187 \times 10^{-14}$ joules, or 0.511 MeV (mega-electronvolts). This is why electron-positron annihilation releases gamma rays of exactly that energy.

Important

The electron's mass is not zero, but it is the smallest mass of any stable, charged particle. Only neutrinos (which are neutral) have smaller masses, and those are still being measured.

A Quick Comparison Table

Particle	Mass (kg)	Relative to Electron
Electron	$9.109 \times 10^{-31}$	1
Proton	$1.673 \times 10^{-27}$	1836
Neutron	$1.675 \times 10^{-27}$	1839

Common Exam Pitfall …

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Electric charge is quantized in integer multiples of the elementary charge $e = 1.602 \times 10^{-19}\ \text{C}$ . Dividing the total charge by $e$ gives 8 electrons on the oil drop.

Why charge comes in packets

Millikan's oil-drop experiment revealed one of nature's most fundamental truths: electric charge cannot take any arbitrary value. It exists only in discrete bundles, each bundle being the charge of a single electron (or proton, with opposite sign). When X-rays ionize air molecules near an oil drop, electrons get transferred to or from the drop, and the drop acquires a net charge that is always an integer multiple of the elementary charge.

The elementary charge—the magnitude of charge on one electron—is

e = 1.602 \times 10^{-19}\ \text{C}

If a drop carries charge $Q$ , then the number of excess (or deficit) electrons is simply

n = \frac{|Q|}{e}

The absolute value accounts for the sign: a negative charge means excess electrons; a positive charge means a deficit.

Finding the number of electrons

1. Identify the given charge

The oil drop has charge $Q = -1.282 \times 10^{-18}\ \text{C}$ . The negative sign tells us the drop has gained electrons (electrons carry negative charge).

2. Take the magnitude

For counting electrons, we work with the magnitude:

|Q| = 1.282 \times 10^{-18}\ \text{C}

3. Divide by the elementary charge

The number of electrons is …

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Q.In Milikan's experiment, static electric charge on the oil drops has been obtained by shining X-rays. If the static electric charge on the oil drop is −1.282×10−18 C-1.282 \times 10^{-18}\ C−1.282×10−18 C, calculate the number of electrons present on it.

Why charge comes in packets

Finding the number of electrons

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Q.In Milikan's experiment, static electric charge on the oil drops has been obtained by shining X-rays. If the static electric charge on the oil drop is $-1.282 \times 10^{-18}\ C$ , calculate the number of electrons present on it.

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