(i) Calculate the number of electrons which will together weigh one gram. (ii) Calculate the mass and charge o

Exercises · 2.1

Q. (i) Calculate the number of electrons which will together weigh one gram.

(ii) Calculate the mass and charge of one mole of electrons.

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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

Students often confuse the mass of an electron with its charge. They are completely different properties:

Mass ( $m_e$ ) tells you how much matter is in the electron — it resists acceleration.
Charge ( $e = 1.602 \times 10^{-19} \text{ C}$ ) tells you how strongly it interacts with electric fields.

Watch out

Never write $m_e = 1.6 \times 10^{-19}$ — that's the charge, not the mass. The mass is $9.1 \times 10^{-31}$ kg.

The Bottom Line

The mass of an electron is $9.1 \times 10^{-31}$ kg — about 1/1836 of a proton's mass. It is a fundamental constant of nature, and its smallness is what makes electrons the nimble, wave-like particles that govern chemistry, electricity, and the behaviour of matter at the atomic scale.

The mass of the electron is one of the foundational constants introduced in the NCERT Class 11 Chemistry chapter on Structure of Atom, and "mass of electron in kg" along with "structure of atom important questions" are frequently searched by students preparing for CBSE boards, JEE Main, and NEET. Confusing this constant with the electron's charge is a classic exam trap, which is why this value is worth memorising precisely alongside the charge-to-mass ratio.

The mass of a single electron is $9.11 \times 10^{-28}$ g. To get one gram, we need about $1.098 \times 10^{27}$ electrons. One mole of electrons has a mass of $5.486 \times 10^{-4}$ g (or $0.5486$ mg) and a charge of $-96485$ C (one Faraday).

The key to both parts is knowing the mass and charge of a single electron. These are fundamental constants, and once you have them, the rest is just careful unit handling and using Avogadro's number.

Mass of one electron: $m_e = 9.11 \times 10^{-28}$ g (or $9.11 \times 10^{-31}$ kg).

Charge of one electron: $e = -1.602 \times 10^{-19}$ C.

The negative sign on the charge tells us the direction of the force, but for calculations of magnitude, we often just use the absolute value $1.602 \times 10^{-19}$ C.

(i) Number of electrons weighing one gram

1. Set up the relation.

If one electron has mass $m_e$ , then $N$ electrons have total mass $M = N \times m_e$ . We want $M = 1$ g.

2. Solve for $N$ .

N = \frac{M}{m_e} = \frac{1 \text{ g}}{9.11 \times 10^{-28} \text{ g/electron}}

3. Do the division.

N = \frac{1}{9.11} \times 10^{28} \approx 0.1098 \times 10^{28} = 1.098 \times 10^{27}

So about $1.1 \times 10^{27}$ electrons are needed to make one gram.

Watch out

A common mistake is to forget that the mass is in grams. If you use $9.11 \times 10^{-31}$ kg (the SI value), you must convert 1 g to $10^{-3}$ kg first. Doing that gives the same answer, but mixing units will give a wrong result.

(ii) Mass and charge of one mole of electrons

A mole is just a specific number of particles: $N_A = 6.022 \times 10^{23}$ particles per mole. So one mole of electrons means $6.022 \times 10^{23}$ electrons.

1. Mass of one mole of electrons.

Multiply the mass of one electron by Avogadro's number:

M_{\text{mole}} = m_e \times N_A = (9.11 \times 10^{-28} \text{ g}) \times (6.022 \times 10^{23})

M_{\text{mole}} = (9.11 \times 6.022) \times 10^{-28+23} = 54.86 \times 10^{-5} \text{ g}

M_{\text{mole}} = 5.486 \times 10^{-4} \text{ g}

That's $0.5486$ milligrams — a tiny mass, as you'd expect for something as light as an electron.

Tip

You can also do this in kg: $9.11 \times 10^{-31} \times 6.022 \times 10^{23} = 5.486 \times 10^{-7}$ kg. Same number, just different units.

2. Charge of one mole of electrons.

Multiply the charge of one electron by Avogadro's number:

Q_{\text{mole}} = e \times N_A = (1.602 \times 10^{-19} \text{ C}) \times (6.022 \times 10^{23})

Q_{\text{mole}} = (1.602 \times 6.022) \times 10^{-19+23} = 9.647 \times 10^{4} \text{ C}

Q_{\text{mole}} = 96470 \text{ C}

This number is famous: it's the Faraday constant ( $F$ ), the charge carried by one mole of electrons. The accepted value is $96485$ C/mol (our slight difference is due to rounding the constants).

F = e \times N_A = 1.602 \times 10^{-19} \times 6.022 \times 10^{23} \approx 96485 \text{ C/mol}

✓Final answer

1.098 \times 10^{27}

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Q.(i) Calculate the number of electrons which will together weigh one gram.

(i) Number of electrons weighing one gram

(ii) Mass and charge of one mole of electrons

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