A certain particle carries $2.5 \times 10^{-16}\ C$ of static electric charge. Calculate the number of electrons present in it.

A certain particle carries 2.5 × 10⁻¹⁶C of static electric charge. Calculate the number of electrons present i

Exercises · 2.38

2.5 \times 10^{-16}\ 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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The charge on a particle is an integer multiple of the elementary charge $e = 1.6 \times 10^{-19}\ \mathrm{C}$ . Dividing the given charge by $e$ gives the number of excess or deficit electrons. The answer is $1.56 \times 10^{3}$ electrons.

The key idea here is quantization of charge. Every static electric charge you observe in nature comes in discrete packets — you cannot have a fraction of an electron’s charge. The smallest free-standing charge is the charge on a single electron (or proton), which has magnitude $e = 1.6 \times 10^{-19}\ \mathrm{C}$ .

So if a particle carries a total charge $Q$ , that charge must be an integer multiple of $e$ :

Q = n e

where $n$ is the number of electrons (if the charge is negative) or the number of protons (if positive). Here the charge is given as $+2.5 \times 10^{-16}\ \mathrm{C}$ — positive, meaning the particle has a deficit of electrons (or an excess of protons). But the question asks for the number of electrons present, which is a bit tricky: it wants the count of electrons that would need to be removed or added to produce that charge. Usually, we interpret this as “how many electrons correspond to this magnitude of charge?”

Let’s work it out.

Write down the given data

Total charge: $Q = 2.5 \times 10^{-16}\ \mathrm{C}$

Charge of one electron: $e = 1.6 \times 10^{-19}\ \mathrm{C}$ (magnitude)
Apply the quantization formula

n = \frac{Q}{e} = \frac{2.5 \times 10^{-16}}{1.6 \times 10^{-19}}

Simplify the division

First, divide the coefficients: $2.5 / 1.6 = 1.5625$

Then handle the powers of ten: $10^{-16} / 10^{-19} = 10^{3}$

So $n = 1.5625 \times 10^{3}$
Round to appropriate significant figures …

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Q.A certain particle carries 2.5×10−16 C2.5 \times 10^{-16}\ C2.5×10−16 C of static electric charge. Calculate the number of electrons present in it.

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Q.A certain particle carries $2.5 \times 10^{-16}\ C$ of static electric charge. Calculate the number of electrons present in it.

Unlock everything free for 14 days