---
title: "Inside the Atom"
book: "School Chemistry — Grades 1 to 12"
subject: chemistry
language: en
chapter: 16
exercises: 12
source: https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom
license: CC-BY-NC-SA-4.0
credit: "One Chemistry Book, One Course (one-course.com)"
---

# Chapter 16 — Inside the Atom

In 1909, in a laboratory in Manchester, a beam of tiny, fast particles was fired at a sheet of gold leaf a few hundred [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) thick. Nearly all of them went straight through, as if the gold were empty. But about one in several thousand bounced back. “It was as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you,” said Ernest Rutherford, whose students had made the experiment. The [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), the uncuttable piece of matter, had a structure — and it was almost entirely empty.

**You already know.**

All matter is made of [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), about a hundred different kinds of them, each with a symbol such as $\ce{H}$, $\ce{C}$, $\ce{O}$, $\ce{Fe}$. [Atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) join into [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule), described by formulas such as $\ce{H2O}$ ([Chapter 11](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#ch-g7-atoms-and-molecules)).

## 16.1 Nucleus and electrons

**Definition 16.1 (Nucleus and electron).**

Every [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) has a tiny, heavy core, the *nucleus*, which carries a positive electric charge. Around it move much lighter particles, the *electrons*, each carrying the same negative charge, $-e$.

**Proposition 16.2 (An atom is neutral).**

An [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) as a whole carries no electric charge: the positive charge of its [nucleus](#def-g9-inside-the-atom-nucleus) is exactly balanced by the negative charges of its [electrons](#def-g9-inside-the-atom-nucleus). The charge $e$ is tiny: $e = 1.60 \times 10^{-19}\,\mathrm{C}$ (the coulomb, unit of charge, is the physics book’s).

![An atom, not to scale. If the nucleus were drawn the size of the red dot, the cloud of electrons would be a few hundred metres across.](https://one-course.com/images/onecourse/chapters/chemistry-1/g9-inside-the-atom/fig-b371b4774665.svg)

*An [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), not to scale. If the [nucleus](#def-g9-inside-the-atom-nucleus) were drawn the size of the red dot, the cloud of [electrons](#def-g9-inside-the-atom-nucleus) would be a few hundred metres across.*

## 16.2 Protons and neutrons

**Definition 16.3 (Proton, neutron, nucleon).**

The [nucleus](#def-g9-inside-the-atom-nucleus) is made of two kinds of particles: *protons*, each carrying the charge $+e$, and *neutrons*, which carry no charge. Protons and neutrons, which have almost the same mass, are together called *nucleons*.

**Definition 16.4 (Atomic number and mass number).**

The number of [protons](#def-g9-inside-the-atom-proton) in a [nucleus](#def-g9-inside-the-atom-nucleus) is the *atomic number*, written $Z$. The number of [nucleons](#def-g9-inside-the-atom-proton) ([protons](#def-g9-inside-the-atom-proton) and [neutrons](#def-g9-inside-the-atom-proton) together) is the *mass number*, written $A$. The number of [neutrons](#def-g9-inside-the-atom-proton) is $N = A - Z$.

**Notation 16.5 (The nuclide symbol).**

An [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) with a given [nucleus](#def-g9-inside-the-atom-nucleus) is written with its symbol, the [mass number](#def-g9-inside-the-atom-atomic-number) at the top left and the [atomic number](#def-g9-inside-the-atom-atomic-number) at the bottom left: $\ce{^{A}_{Z}X}$. For example $\ce{^{12}_{6}C}$ has 6 [protons](#def-g9-inside-the-atom-proton) and $12 - 6 =
6$ [neutrons](#def-g9-inside-the-atom-proton); $\ce{^{56}_{26}Fe}$ has 26 [protons](#def-g9-inside-the-atom-proton) and 30 [neutrons](#def-g9-inside-the-atom-proton).

**Method 16.6 (Reading a nuclide symbol).**

For $\ce{^{A}_{Z}X}$:

1. [protons](#def-g9-inside-the-atom-proton) : $Z$ ;
2. [neutrons](#def-g9-inside-the-atom-proton) : $A - Z$ ;
3. [electrons](#def-g9-inside-the-atom-nucleus) of the neutral [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) : $Z$ , the same as the [protons](#def-g9-inside-the-atom-proton) .

For $\ce{^{23}_{11}Na}$: 11 [protons](#def-g9-inside-the-atom-proton), 12 [neutrons](#def-g9-inside-the-atom-proton), 11 [electrons](#def-g9-inside-the-atom-nucleus).

![Reading a nuclide symbol: this chlorine atom has 17 protons, 35 - 17 = 18 neutrons, and 17 electrons when neutral.](https://one-course.com/images/onecourse/chapters/chemistry-1/g9-inside-the-atom/fig-a3fcd3778ff8.svg)

*Reading a nuclide symbol: this chlorine [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) has 17 [protons](#def-g9-inside-the-atom-proton), $35 - 17 = 18$ [neutrons](#def-g9-inside-the-atom-proton), and 17 [electrons](#def-g9-inside-the-atom-nucleus) when neutral.*

## 16.3 The chemical element and its isotopes

**Definition 16.7 (Chemical element).**

A *chemical element* is the set of all the [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), and of all the charged [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) made from them, that have the same [atomic number](#def-g9-inside-the-atom-atomic-number) $Z$. Each element has a name and a symbol: every [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) with 6 [protons](#def-g9-inside-the-atom-proton) is a carbon [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), $\ce{C}$; every [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) with 8 [protons](#def-g9-inside-the-atom-proton) is an oxygen [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), $\ce{O}$.

**Definition 16.8 (Isotopes).**

[Atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) of the same element that have different numbers of [neutrons](#def-g9-inside-the-atom-proton), and so different [mass numbers](#def-g9-inside-the-atom-atomic-number), are *isotopes* of that element. They have the same $Z$ and different $A$.

**Example 16.9 (Isotopes of carbon and of hydrogen).**

Natural carbon is about $98.9\,\%$ carbon-12, $\ce{^{12}_{6}C}$, and $1.1\,\%$ carbon-13, $\ce{^{13}_{6}C}$, with a trace of carbon-14, $\ce{^{14}_{6}C}$, whose slow change into another [nucleus](#def-g9-inside-the-atom-nucleus) is used to date ancient wood and bones (radioactivity belongs to the physics book). Hydrogen has three [isotopes](#def-g9-inside-the-atom-isotope): $\ce{^{1}_{1}H}$, with no [neutron](#def-g9-inside-the-atom-proton) at all, the commonest by far; deuterium $\ce{^{2}_{1}H}$, a few [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) in every hundred thousand; and tritium $\ce{^{3}_{1}H}$.

**Proposition 16.10 (Isotopes behave alike in chemistry).**

The chemistry of an [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) depends on its [electrons](#def-g9-inside-the-atom-nucleus), and the [isotopes](#def-g9-inside-the-atom-isotope) of an element have the same number of [electrons](#def-g9-inside-the-atom-nucleus). [Isotopes](#def-g9-inside-the-atom-isotope) therefore react in the same way: water made with deuterium looks and behaves almost exactly like ordinary water.

![The nuclei of the three isotopes of hydrogen: one proton each, and 0, 1 or 2 neutrons.](https://one-course.com/images/onecourse/chapters/chemistry-1/g9-inside-the-atom/fig-384be161bdee.svg)

*The nuclei of the three [isotopes](#def-g9-inside-the-atom-isotope) of hydrogen: one [proton](#def-g9-inside-the-atom-proton) each, and 0, 1 or 2 [neutrons](#def-g9-inside-the-atom-proton).*

## 16.4 Sizes and masses

**Proposition 16.11 (The nucleus is tiny and holds almost all the mass).**

An [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) measures about $10^{-10}\,\mathrm{m}$ across; its [nucleus](#def-g9-inside-the-atom-nucleus), about $10^{-15}\,\mathrm{m}$ to $10^{-14}\,\mathrm{m}$: some ten thousand to a hundred thousand times smaller. The masses of the particles are

$$
m_p = 1.673 \times 10^{-27}\,\mathrm{kg},\qquad m_n = 1.675 \times 10^{-27}\,\mathrm{kg},\qquad
  m_e = 9.11 \times 10^{-31}\,\mathrm{kg}.
$$

A [proton](#def-g9-inside-the-atom-proton) is about 1836 times heavier than an [electron](#def-g9-inside-the-atom-nucleus), so more than $99.9\,\%$ of the mass of an [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) is in its [nucleus](#def-g9-inside-the-atom-nucleus).

**Example 16.12 (A marble in a stadium).**

If the [nucleus](#def-g9-inside-the-atom-nucleus) of an [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) were a marble $1\,\mathrm{cm}$ across, the [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) would be about $1\,\mathrm{cm} \times 100\,000 = 1\,\mathrm{km}$ across: a marble in the middle of a huge stadium, with a few specks of dust — the [electrons](#def-g9-inside-the-atom-nucleus) — whirling around the stands. Matter is mostly empty space.

**Method 16.13 (The mass of an atom).**

Since [protons](#def-g9-inside-the-atom-proton) and [neutrons](#def-g9-inside-the-atom-proton) have nearly the same mass and [electrons](#def-g9-inside-the-atom-nucleus) are very light, the mass of an [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) is close to $A \times
1.67 \times 10^{-27}\,\mathrm{kg}$, where $A$ is its [mass number](#def-g9-inside-the-atom-atomic-number). A carbon-12 [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom): $12 \times 1.67 \times 10^{-27} = 2.00 \times 10^{-26}\,\mathrm{kg}$.

## 16.5 A short history of the atomic model

**History — From the uncuttable to the nucleus, 1897–1932.**

In 1897 J. J. Thomson discovered the [electron](#def-g9-inside-the-atom-nucleus), a particle far lighter than any [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom): [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) could be cut after all. He pictured the [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) as a ball of positive matter studded with [electrons](#def-g9-inside-the-atom-nucleus). In 1909–1911 the gold-foil experiment of Rutherford’s team showed that the positive charge and almost all the mass sit in a tiny [nucleus](#def-g9-inside-the-atom-nucleus). In 1913 Niels Bohr proposed that the [electrons](#def-g9-inside-the-atom-nucleus) occupy fixed energy levels around it, and in 1932 James Chadwick found the [neutron](#def-g9-inside-the-atom-proton).

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g9-inside-the-atom/img-3af935b63df5.jpg)

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g9-inside-the-atom/fig-b627ccd823e4.svg)

*Ernest Rutherford (1871–1937).*

*The gold-foil experiment: most particles pass straight through; a few are deflected; a very few bounce back from a [nucleus](#def-g9-inside-the-atom-nucleus).*

## 16.6 Exercises

**Exercise 16.1 ★.**

Name the particles of the [nucleus](#def-g9-inside-the-atom-nucleus) and the particles around it, with the sign of their charge.

**Solution of Exercise 16.1.**

In the [nucleus](#def-g9-inside-the-atom-nucleus): [protons](#def-g9-inside-the-atom-proton) (positive) and [neutrons](#def-g9-inside-the-atom-proton) (no charge). Around it: [electrons](#def-g9-inside-the-atom-nucleus) (negative).

**Exercise 16.2 ★.**

Give the number of [protons](#def-g9-inside-the-atom-proton), [neutrons](#def-g9-inside-the-atom-proton) and [electrons](#def-g9-inside-the-atom-nucleus) of $\ce{^{16}_{8}O}$, $\ce{^{27}_{13}Al}$ and $\ce{^{40}_{20}Ca}$.

**Solution of Exercise 16.2.**

$\ce{^{16}_{8}O}$: 8 [protons](#def-g9-inside-the-atom-proton), 8 [neutrons](#def-g9-inside-the-atom-proton), 8 [electrons](#def-g9-inside-the-atom-nucleus). $\ce{^{27}_{13}Al}$: 13, 14, 13. $\ce{^{40}_{20}Ca}$: 20, 20, 20.

**Exercise 16.3 ★.**

Why is an [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) electrically neutral?

**Solution of Exercise 16.3.**

It has as many [electrons](#def-g9-inside-the-atom-nucleus) (charge $-e$ each) as [protons](#def-g9-inside-the-atom-proton) (charge $+e$ each): the charges cancel.

**Exercise 16.4 ★.**

An [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) has 26 [protons](#def-g9-inside-the-atom-proton) and 30 [neutrons](#def-g9-inside-the-atom-proton). Write its nuclide symbol (the element is iron, $\ce{Fe}$).

**Solution of Exercise 16.4.**

$A = 26 + 30 = 56$: $\ce{^{56}_{26}Fe}$.

**Exercise 16.5 ★★.**

Are $\ce{^{35}_{17}Cl}$ and $\ce{^{37}_{17}Cl}$ the same element? Are they [isotopes](#def-g9-inside-the-atom-isotope)? Explain.

**Solution of Exercise 16.5.**

Yes: both have $Z = 17$, so both are chlorine. They have different [mass numbers](#def-g9-inside-the-atom-atomic-number) (18 and 20 [neutrons](#def-g9-inside-the-atom-proton)): they are [isotopes](#def-g9-inside-the-atom-isotope).

**Exercise 16.6 ★★.**

Are $\ce{^{14}_{6}C}$ and $\ce{^{14}_{7}N}$ [isotopes](#def-g9-inside-the-atom-isotope)? Explain.

**Solution of Exercise 16.6.**

No: they have different [atomic numbers](#def-g9-inside-the-atom-atomic-number) (6 and 7), so they are different elements, carbon and nitrogen. [Isotopes](#def-g9-inside-the-atom-isotope) have the same $Z$.

**Exercise 16.7 ★★.**

Compute, in scientific notation, the approximate mass of an [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) of $\ce{^{56}_{26}Fe}$.

**Solution of Exercise 16.7.**

$56 \times 1.67 \times 10^{-27} \approx 9.35 \times 10^{-26}\,\mathrm{kg}$.

**Exercise 16.8 ★★.**

In the gold-foil experiment, why do most particles go straight through the gold?

**Solution of Exercise 16.8.**

An [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) is mostly empty space: the [nucleus](#def-g9-inside-the-atom-nucleus) is tiny, so most particles meet no [nucleus](#def-g9-inside-the-atom-nucleus) on their way and pass straight through.

**Exercise 16.9 ★★.**

How many times smaller than an [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) ($10^{-10}\,\mathrm{m}$) is a [nucleus](#def-g9-inside-the-atom-nucleus) of $10^{-15}\,\mathrm{m}$? Write the answer as a power of ten.

**Solution of Exercise 16.9.**

$10^{-10} / 10^{-15} = 10^{5}$: a hundred thousand times smaller.

**Exercise 16.10 ★★.**

Why do the [isotopes](#def-g9-inside-the-atom-isotope) of an element have the same chemistry?

**Solution of Exercise 16.10.**

Chemistry depends on the [electrons](#def-g9-inside-the-atom-nucleus), and [isotopes](#def-g9-inside-the-atom-isotope) of an element have the same number of [electrons](#def-g9-inside-the-atom-nucleus) (the same $Z$).

**Exercise 16.11 ★★★.**

An iron [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) has 26 [electrons](#def-g9-inside-the-atom-nucleus). Compute their total mass, then the fraction of the mass of a $\ce{^{56}_{26}Fe}$ [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) that they make up (use the mass found in exercise 7).

**Solution of Exercise 16.11.**

$26 \times 9.11 \times 10^{-31} = 2.37 \times 10^{-29}\,\mathrm{kg}$. Fraction: $2.37 \times 10^{-29} / 9.35 \times 10^{-26} \approx 2.5 \times
10^{-4}$, about $0.025\,\%$ of the mass.

**Exercise 16.12 ★★★.**

Natural copper is $69.15\,\%$ copper-63 and $30.85\,\%$ copper-65. Among 10 000 copper [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), how many are of each [isotope](#def-g9-inside-the-atom-isotope)? What is the average number of [nucleons](#def-g9-inside-the-atom-proton) per copper [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom)?

**Solution of Exercise 16.12.**

6915 copper-63 [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) and 3085 copper-65 [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom). Average: $(6915 \times 63 + 3085 \times 65)/10\,000 = 63.6$ [nucleons](#def-g9-inside-the-atom-proton).

## 16.7 Problem: Weighing Chlorine

**Problem 16.1.**

Weekend problem — two isotopes of chlorine, the mass of each atom, and the average mass of a chlorine atom

Natural chlorine is a [mixture](https://one-course.com/books/chemistry/1/en/chapter/8-pure-substances-and-mixtures#def-g6-pure-substances-and-mixtures-mixture) of two [isotopes](#def-g9-inside-the-atom-isotope), chlorine-35 and chlorine-37: out of 1000 chlorine [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), about 758 are chlorine-35 and 242 chlorine-37. Take the mass of a [nucleon](#def-g9-inside-the-atom-proton) as $1.67 \times 10^{-27}\,\mathrm{kg}$ and the mass of an [electron](#def-g9-inside-the-atom-nucleus) as $9.11 \times 10^{-31}\,\mathrm{kg}$. The [atomic number](#def-g9-inside-the-atom-atomic-number) of chlorine is 17.

**Part I — Two nuclei.**

1. Write the nuclide symbols of the two [isotopes](#def-g9-inside-the-atom-isotope) .
2. Give the number of [protons](#def-g9-inside-the-atom-proton) , [neutrons](#def-g9-inside-the-atom-proton) and [electrons](#def-g9-inside-the-atom-nucleus) of each.
3. Why are both called chlorine? Why are they [isotopes](#def-g9-inside-the-atom-isotope) ?
4. Will a sample of chlorine-37 react with sodium the same way as a sample of chlorine-35? Explain.

**Part II — The mass of each [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom).**

5. Compute the mass of the [nucleus](#def-g9-inside-the-atom-nucleus) of a chlorine-35 [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) .
6. Compute the mass of the 17 [electrons](#def-g9-inside-the-atom-nucleus) , and check that it can be neglected beside the [nucleus](#def-g9-inside-the-atom-nucleus) .
7. Compute the mass of a chlorine-37 [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) .
8. How many chlorine-35 [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) would weigh $1\,\mathrm{g}$ ? Give the answer in scientific notation.

**Part III — The average [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom).**

9. What percentage of chlorine [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) are chlorine-35? Chlorine-37?
10. In 1000 [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) of natural chlorine, compute the total mass of the chlorine-35 [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) and of the chlorine-37 [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) .
11. Compute the mass of these 1000 [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) .
12. Deduce the average mass of a chlorine [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) .

**Solution of Problem 16.1.**

**1.** $\ce{^{35}_{17}Cl}$ and $\ce{^{37}_{17}Cl}$.

**2.** Chlorine-35: 17 [protons](#def-g9-inside-the-atom-proton), 18 [neutrons](#def-g9-inside-the-atom-proton), 17 [electrons](#def-g9-inside-the-atom-nucleus). Chlorine-37: 17 [protons](#def-g9-inside-the-atom-proton), 20 [neutrons](#def-g9-inside-the-atom-proton), 17 [electrons](#def-g9-inside-the-atom-nucleus).

**3.** Both have 17 [protons](#def-g9-inside-the-atom-proton), so both are the element chlorine; they differ only by their number of [neutrons](#def-g9-inside-the-atom-proton), so they are [isotopes](#def-g9-inside-the-atom-isotope).

**4.** Yes: chemistry depends on the [electrons](#def-g9-inside-the-atom-nucleus), and both have 17.

**5.** $35 \times 1.67 \times 10^{-27} = 5.845 \times 10^{-26}\,\mathrm{kg}$.

**6.** $17 \times 9.11 \times 10^{-31} = 1.55 \times 10^{-29}\,\mathrm{kg}$: about 4000 times less than the [nucleus](#def-g9-inside-the-atom-nucleus), negligible.

**7.** $37 \times 1.67 \times 10^{-27} = 6.179 \times 10^{-26}\,\mathrm{kg}$.

**8.** $1\,\mathrm{g} = 10^{-3}\,\mathrm{kg}$; $10^{-3} / 5.845 \times
10^{-26} \approx 1.71 \times 10^{22}$ [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom).

**9.** $75.8\,\%$ and $24.2\,\%$.

**10.** $758 \times 5.845 \times 10^{-26} = 4.430 \times 10^{-23}\,\mathrm{kg}$; $242 \times 6.179 \times 10^{-26} = 1.495 \times 10^{-23}\,\mathrm{kg}$.

**11.** $4.430 \times 10^{-23} + 1.495 \times 10^{-23} =
5.925 \times 10^{-23}\,\mathrm{kg}$.

**12.** $5.925 \times 10^{-23} / 1000 \approx
5.93 \times 10^{-26}\,\mathrm{kg}$: the average mass of a chlorine [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom).