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Atoms Honors: Isotopes and Nuclear Notation Study Guide
Atoms Honors: Isotopes and Nuclear Notation
Atomic Structure
An atom contains three main subatomic particles:
The nucleus contains protons and neutrons. Electrons occupy the space surrounding the nucleus.
Atomic Number, Mass Number, and Atomic Mass
Atomic number \(Z\)
The atomic number equals the number of protons:
\[
Z = \text{number of protons}
\]
The atomic number identifies the element. If an atom has \(8\) protons, it is always oxygen.
Mass number \(A\)
The mass number is the total number of protons and neutrons:
\[
A = p + n
\]
where \(p\) is protons and \(n\) is neutrons.
Therefore:
\[
n = A - Z
\]
Average atomic mass
The atomic mass shown on the periodic table is usually a weighted average of the masses of the element's naturally occurring isotopes. It is commonly a decimal, unlike a mass number, which is a whole number.
Isotopes
Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons.
Because isotopes have the same number of protons, they have the same atomic number. Because they have different numbers of neutrons, they have different mass numbers.
Example:
Carbon-12: \(6\) protons and \(6\) neutrons
Carbon-13: \(6\) protons and \(7\) neutrons
Carbon-14: \(6\) protons and \(8\) neutrons
These are all carbon because each has \(6\) protons.
Nuclear Form
The nuclear form, also called nuclear notation, is written as:
\[
{}^{A}_{Z}\mathrm{X}
\]
\(\mathrm{X}\) = element symbol
\(A\) = mass number, written at the upper left
\(Z\) = atomic number, written at the lower left
Example:
\[
{}^{23}_{11}\mathrm{Na}
\]
This represents sodium-23.
Calculations:
Protons: \(p = Z = 11\)
Neutrons: \(n = A - Z = 23 - 11 = 12\)
Electrons in a neutral atom: \(e = 11\)
Hyphen Form
The hyphen form writes the element name followed by its mass number:
\[
\text{element name}-\text{mass number}
\]
Examples:
\({}^{23}_{11}\mathrm{Na}\) becomes sodium-23
\({}^{35}_{17}\mathrm{Cl}\) becomes chlorine-35
\({}^{14}_{6}\mathrm{C}\) becomes carbon-14
The number after the hyphen is always the mass number, not the atomic number.
Finding Protons, Neutrons, and Electrons
For a neutral atom:
\[
p = Z
\]
\[
n = A - Z
\]
\[
e = p = Z
\]
Example 1: \({}^{27}_{13}\mathrm{Al}\)
Protons: \(13\)
Neutrons: \(27 - 13 = 14\)
Electrons: \(13\)
Example 2: bromine-80
Bromine has atomic number \(35\).
Mass number: \(80\)
Protons: \(35\)
Neutrons: \(80 - 35 = 45\)
Electrons: \(35\) if neutral
Nuclear form: \({}^{80}_{35}\mathrm{Br}\)
Ions and Electron Calculations
An ion is an atom with a charge because it has gained or lost electrons. The number of protons does not change when an ion forms.
Use:
\[
\text{charge} = p - e
\]
To find electrons:
\[
e = p - \text{charge}
\]
Be careful with negative charges: subtracting a negative number adds electrons.
Positive ion example: \(\mathrm{Mg}^{2+}\)
Magnesium has \(12\) protons.
\[
e = 12 - (+2) = 10
\]
So \(\mathrm{Mg}^{2+}\) has \(12\) protons and \(10\) electrons.
Negative ion example: \(\mathrm{O}^{2-}\)
Oxygen has \(8\) protons.
\[
e = 8 - (-2) = 10
\]
So \(\mathrm{O}^{2-}\) has \(8\) protons and \(10\) electrons.
Isotope Calculations
Finding an isotope's neutrons
For \({}^{A}_{Z}\mathrm{X}\):
\[
n = A - Z
\]
Example: How many neutrons are in uranium-238?
Uranium has atomic number \(92\).
\[
n = 238 - 92 = 146
\]
Uranium-238 has \(146\) neutrons.
Finding the mass number
If you know the protons and neutrons:
\[
A = p + n
\]
Example: An atom has \(17\) protons and \(18\) neutrons.
\[
A = 17 + 18 = 35
\]
The atom is chlorine-35.
Calculating average atomic mass
If isotope percentages are given, use:
\[
\text{average atomic mass} = (m1)(a1) + (m2)(a2) + \cdots
\]
Convert each percent to a decimal before multiplying.
Example:
An element has two isotopes:
Isotope 10: mass \(10.0\) amu and abundance \(20\% = 0.20\)
Isotope 11: mass \(11.0\) amu and abundance \(80\% = 0.80\)
\[
(10.0)(0.20) + (11.0)(0.80) = 2.0 + 8.8 = 10.8\text{ amu}
\]
The average atomic mass is \(10.8\) amu.
How to Read Any Isotope Question
Use this order:
Identify the element from its symbol or atomic number.
Find the atomic number \(Z\), which gives protons.
Find the mass number \(A\), which gives protons plus neutrons.
Subtract \(A - Z\) to find neutrons.
Check the charge to find electrons.
Write the answer in nuclear form or hyphen form if requested.
Common Mistakes
Confusing atomic number with mass number.
Using the periodic-table decimal as the mass number without rounding when the problem requires a specific isotope.
Changing the number of protons when an ion forms.
Forgetting that a positive ion has fewer electrons.
Forgetting that a negative ion has more electrons.
Writing the atomic number after the hyphen instead of the mass number.
Treating isotopes as different elements. Isotopes are still the same element because they have the same number of protons.
Practice Questions
For \({}^{39}_{19}\mathrm{K}\), find the numbers of protons, neutrons, and electrons.
Write nuclear form and hyphen form for an atom with \(16\) protons and \(18\) neutrons.
How many electrons are in \(\mathrm{Al}^{3+}\)?
How many electrons are in \(\mathrm{F}^{-}\)?
An isotope has \(26\) protons and \(30\) neutrons. Identify the element and write its hyphen form.
Calculate the average atomic mass of isotopes with masses \(24.0\) amu and \(25.0\) amu if their abundances are \(75\%\) and \(25\%\), respectively.
Answer Key
\({}^{39}_{19}\mathrm{K}\): \(19\) protons, \(20\) neutrons, \(19\) electrons.
Atomic number \(16\) is sulfur; mass number \(16 + 18 = 34\). Nuclear form: \({}^{34}_{16}\mathrm{S}\). Hyphen form: sulfur-34.
Aluminum has \(13\) protons, so \(\mathrm{Al}^{3+}\) has \(13 - 3 = 10\) electrons.
Fluorine has \(9\) protons, so \(\mathrm{F}^{-}\) has \(9 - (-1) = 10\) electrons.
Atomic number \(26\) is iron; mass number \(26 + 30 = 56\). Hyphen form: iron-56.
\((24.0)(0.75) + (25.0)(0.25) = 18.0 + 6.25 = 24.25\text{ amu}\).
Must-Know Formulas
\[
A = p + n
\]
\[
n = A - Z
\]
\[
p = Z
\]
\[
\text{charge} = p - e
\]
\[
e = p - \text{charge}
\]
\[
\text{average atomic mass} = \sum(\text{isotope mass})(\text{decimal abundance})
Interactive Self-Check
Try each question before opening the answer.
<details>
<summary>1. For \({}^{39}_{19}\mathrm{K}\), how many protons, neutrons, and electrons are there?</summary>
Answer: 19 protons, \(39-19=20\) neutrons, and 19 electrons because the atom is neutral.
</details>
<details>
<summary>2. How many electrons are in \(\mathrm{O}^{2-}\)?</summary>
Answer: 10 electrons. Oxygen has 8 protons, so \(e=8-(-2)=10\).
</details>
<details>
<summary>3. An atom has 17 protons and 18 neutrons. What is its nuclear form and hyphen form?</summary>
Answer: \({}^{35}_{17}\mathrm{Cl}\), or chlorine-35.
</details>
<details>
<summary>4. An element has isotopes of 10.0 amu at 20% abundance and 11.0 amu at 80% abundance. What is its average atomic mass?</summary>
Answer: \((10.0)(0.20)+(11.0)(0.80)=10.8\text{ amu}\).
</details>
Quiz Mode
Use this page with a study partner—or ask in chat: “Quiz me on this page.” You will receive one question at a time, with feedback after each answer. Start now:
Question 1: For \({}^{27}_{13}\mathrm{Al}\), how many protons, neutrons, and electrons does a neutral atom have?
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