1. Overview
Isotopes explain why the atoms of a single element are not all identical in mass, despite behaving the same way in chemical reactions. Understanding isotopes is crucial for calculating Relative Atomic Mass ($A_r$) and explaining the nuclear stability used in medicine and energy production.
Key Definitions
- Isotopes: Different atoms of the same element which have the same number of protons but different numbers of neutrons.
- Proton Number (Atomic Number): The number of protons in the nucleus of an atom.
- Nucleon Number (Mass Number): The total number of protons and neutrons in the nucleus of an atom.
- Relative Atomic Mass ($A_r$): The average mass of naturally occurring atoms of an element on a scale where the $^{12}\text{C}$ atom has a mass of exactly 12 units.
Core Content
Understanding Isotopes
Since the identity of an element is determined solely by its proton number, isotopes are versions of the same element that simply "weigh" different amounts because their nuclei contain different numbers of neutrons.
Example: Carbon Isotopes
- Carbon-12 ($^{12}\text{C}$): 6 protons, 6 neutrons, 6 electrons.
- Carbon-14 ($^{14}\text{C}$): 6 protons, 8 neutrons, 6 electrons.
Interpreting Symbols and Ions
Symbols are written in the format: $^{A}_{Z}X^{charge}$
- $A$ = Nucleon number (top)
- $Z$ = Proton number (bottom)
- $X$ = Chemical symbol
Examples:
- Atom: $^{12}_{6}\text{C}$ has 6 protons and 6 neutrons ($12 - 6 = 6$).
- Ion: $^{35}_{17}\text{Cl}^{-}$
- Protons: 17
- Neutrons: 18 ($35 - 17 = 18$)
- Electrons: 18 (The "$-$" sign means it has gained one electron: $17 + 1 = 18$).
Extended Content (Extended Curriculum Only)
Chemical and Physical Properties
- Chemical Properties: Isotopes of the same element have identical chemical properties. This is because chemical reactions involve electrons; since isotopes have the same number of electrons and the same electronic configuration, they react in exactly the same way.
- Physical Properties: Isotopes show slight differences in physical properties, such as density, melting point, and boiling point, because these properties are affected by the mass of the atom.
Example Reaction (State symbols included): Whether using $^{35}\text{Cl}$ or $^{37}\text{Cl}$, the reaction with Hydrogen is identical:
- Word Equation: hydrogen (g) + chlorine (g) → hydrogen chloride (g)
- Symbol Equation: $\text{H}_2\text{(g)} + \text{Cl}_2\text{(g)} \rightarrow 2\text{HCl(g)}$
Calculating Relative Atomic Mass ($A_r$)
Because elements exist as mixtures of isotopes, the value on the Periodic Table is a weighted average.
Formula: $$A_r = \frac{(\text{mass of isotope 1} \times \text{abundance}) + (\text{mass of isotope 2} \times \text{abundance})}{100}$$
Worked Example: Naturally occurring Chlorine contains 75% $^{35}\text{Cl}$ and 25% $^{37}\text{Cl}$. Calculate the $A_r$.
- $(35 \times 75) = 2625$
- $(37 \times 25) = 925$
- $2625 + 925 = 3550$
- $3550 / 100 = 35.5$ Answer: $A_r$ of $\text{Cl} = 35.5$
Key Equations
- Nucleon Number ($A$) = number of protons + number of neutrons
- Number of Neutrons = $A - Z$ (Nucleon number - Proton number)
- Relative Atomic Mass ($A_r$):
$$\sum \frac{(\text{Isotope mass} \times \text{Isotope percentage abundance})}{100}$$
- Units: $A_r$ is a ratio and has no units.
Common Mistakes to Avoid
- ❌ Wrong: Isotopes have different chemical properties because they have different masses.
- ✅ Right: Isotopes have the same chemical properties because they have the same electronic configuration.
- ❌ Wrong: Thinking that ions have a different number of protons or neutrons.
- ✅ Right: Only the number of electrons changes when an atom becomes an ion.
- ❌ Wrong: Forgetting to divide by 100 when calculating $A_r$ from percentage abundances.
Exam Tips
- Command Words:
- "State": Give a brief, factual answer (e.g., "State the number of protons in $^{14}\text{C}$" → Answer: 6).
- "Explain": You must give a reason. If asked why isotopes react the same way, explain that they have the same number of outer shell electrons.
- "Show": Always write out the full calculation for $A_r$ to gain method marks, even if you make a calculator error.
- Question Types: Expect to fill in tables comparing protons, neutrons, and electrons for various atoms and ions.
- Real-world Contexts: Look out for questions involving "nuclear" isotopes (used as fuel or in medicine) versus "stable" isotopes.
- Typical Values: $A_r$ values often end in .0 or .5 (like Chlorine 35.5 or Copper 63.5). If your calculated value is nowhere near the mass numbers given in the question, re-check your division.
Exam-Style Questions
Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0620 Theory papers.
Exam-Style Question 1 — Short Answer [5 marks]
Question:
Copper exists as two isotopes, copper-63 ($^{63}Cu$) and copper-65 ($^{65}Cu$).
(a) Define the term isotopes. [2]
(b) State two differences between an atom of $^{63}Cu$ and an atom of $^{65}Cu$. [2]
(c) Explain why the isotopes of copper have the same chemical properties. [1]
Worked Solution:
(a)
- Isotopes are atoms of the same element... ...that have the same number of protons but different numbers of neutrons. [This definition covers the key points about isotopes]
How to earn full marks:
- State "atoms of the same element".
- State that they have the same number of protons and different numbers of neutrons.
(b)
The number of neutrons is different... $^{65}Cu$ has two more neutrons than $^{63}Cu$. [State the difference in neutron number]
The mass number is different... $^{65}Cu$ has a greater mass number than $^{63}Cu$. [State the difference in mass number]
How to earn full marks:
- State that the number of neutrons is different.
- State that the mass number is different.
(c)
- Chemical properties depend on the number of electrons... ...isotopes of the same element have the same number of electrons and therefore the same electronic configuration. [Explain the link between electrons, electronic configuration, and chemical properties]
How to earn full marks:
- Link chemical properties to the number of electrons.
- State that isotopes have the same number of electrons and the same electronic configuration.
Common Pitfall: Make sure you provide a complete definition of isotopes, including both the similarities and differences in their atomic structure. Also, remember that chemical properties are determined by the number of electrons, not neutrons.
Exam-Style Question 2 — Short Answer [6 marks]
Question:
Chlorine exists as two isotopes: chlorine-35 ($^{35}Cl$) and chlorine-37 ($^{37}Cl$). A sample of chlorine contains 75% $^{35}Cl$ and 25% $^{37}Cl$.
(a) Calculate the relative atomic mass ($A_r$) of chlorine in this sample. [3]
(b) Complete the table to show the number of protons, neutrons and electrons in an ion of $^{35}Cl^-$. [3]
| Particle | Number |
|---|---|
| Protons | |
| Neutrons | |
| Electrons |
Worked Solution:
(a)
The relative atomic mass is a weighted average... $A_r = \frac{(75 \times 35) + (25 \times 37)}{100}$ [Correct formula for weighted average]
Calculate the numerator... $A_r = \frac{2625 + 925}{100}$ [Correct calculation of the numerator]
Calculate the final answer... $A_r = \frac{3550}{100} = \boxed{35.5}$ [Correct calculation of the relative atomic mass]
How to earn full marks:
- Show the working of the weighted average calculation.
- Correct numerator in the calculation.
- Correct final answer of 35.5 (no units needed).
(b)
Chlorine has an atomic number of 17, so it has 17 protons... Protons = 17 [Correct number of protons]
Mass number minus atomic number equals number of neutrons... Neutrons = 35 - 17 = 18 [Correct number of neutrons]
A negative ion has gained one electron... Electrons = 17 + 1 = 18 [Correct number of electrons]
How to earn full marks:
- Correct number of protons (17).
- Correct number of neutrons (18).
- Correct number of electrons (18).
Common Pitfall: Remember that the number of protons defines the element. When dealing with ions, make sure to adjust the number of electrons accordingly, adding electrons for negative ions and subtracting for positive ions.
Exam-Style Question 3 — Extended Response [9 marks]
Question:
Magnesium has three naturally occurring isotopes: magnesium-24 ($^{24}Mg$), magnesium-25 ($^{25}Mg$), and magnesium-26 ($^{26}Mg$). A mass spectrometer analysis of a sample of magnesium gives the following data:
| Isotope | Relative Abundance (%) |
|---|---|
| $^{24}Mg$ | 79.0 |
| $^{25}Mg$ | 10.0 |
| $^{26}Mg$ | 11.0 |
(a) Define the term relative atomic mass. [2]
(b) Calculate the relative atomic mass of magnesium in this sample, giving your answer to two decimal places. [4]
(c) Suggest one reason why it is important to know the relative abundance of different isotopes of an element. [1]
(d) Magnesium reacts with hydrochloric acid to produce magnesium chloride and hydrogen gas. $$Mg(s) + 2HCl(aq) \rightarrow MgCl_2(aq) + H_2(g)$$ State how the rate of this reaction would be affected if magnesium consisting only of the isotope $^{24}Mg$ was used instead of the naturally occurring mixture of isotopes. Explain your answer. [2]
Worked Solution:
(a)
- Relative atomic mass is the weighted average mass... ...of all the isotopes of an element, relative to 1/12th the mass of an atom of carbon-12. [Complete definition]
How to earn full marks:
- State the weighted average mass of isotopes.
- State that it is relative to 1/12th the mass of carbon-12.
(b)
Use the formula for weighted average... $A_r = \frac{(79.0 \times 24) + (10.0 \times 25) + (11.0 \times 26)}{100}$ [Correct formula for weighted average]
Calculate the numerator... $A_r = \frac{1896 + 250 + 286}{100}$ [Correct calculation of the numerator]
Calculate the final answer... $A_r = \frac{2432}{100} = \boxed{24.32}$ [Correct calculation of the relative atomic mass]
Round to two decimal places... $A_r = \boxed{24.32}$ [Correct rounding]
How to earn full marks:
- Show the working of the weighted average calculation.
- Correct numerator in the calculation.
- Correct final answer of 24.32 (no units needed).
(c)
- Knowing isotopic abundance helps in various applications... ...for example, to determine the age of rocks (radioactive dating) or to trace the origin of materials. [Suggest a valid application]
How to earn full marks:
- Suggest a valid application, such as radioactive dating or tracing origins.
(d)
- The rate would be unaffected... ...because isotopes have the same chemical properties as they have the same number of electrons. [State no effect with valid reasoning]
How to earn full marks:
- State that the rate of reaction would be unaffected.
- Explain that isotopes have the same chemical properties due to the same number of electrons.
Common Pitfall: When calculating relative atomic mass, double-check that you're using the correct percentages and masses for each isotope. Also, remember that the chemical properties of isotopes are identical due to their identical electron configurations.
Exam-Style Question 4 — Extended Response [10 marks]
Question:
Sulfur exists in several isotopic forms. Consider two isotopes of sulfur: sulfur-32 ($^{32}S$) and sulfur-34 ($^{34}S$).
(a) State the number of protons, neutrons, and electrons in a neutral atom of $^{32}S$. [3]
(b) The relative atomic mass of sulfur is 32.1. Explain why the relative atomic mass is closer to 32 than to 34, given that sulfur has only these two isotopes. [2]
(c) Sulfur dioxide ($SO_2$) is a gas formed during the combustion of fossil fuels containing sulfur. It can react with water in the atmosphere to form acid rain.
(i) Complete the dot-and-cross diagram to show the electron arrangement in a molecule of sulfur dioxide ($SO_2$). Only show the outer shell electrons. Sulfur has 6 outer shell electrons and oxygen has 6 outer shell electrons. [3]
(ii) Predict the effect of acid rain on limestone buildings. Explain your answer. [2]
Worked Solution:
(a)
Sulfur has an atomic number of 16, so it has 16 protons... Protons = 16 [Correct number of protons]
Mass number minus atomic number equals number of neutrons... Neutrons = 32 - 16 = 16 [Correct number of neutrons]
In a neutral atom, the number of electrons equals the number of protons... Electrons = 16 [Correct number of electrons]
How to earn full marks:
- Correct number of protons (16).
- Correct number of neutrons (16).
- Correct number of electrons (16).
(b)
- The relative atomic mass is a weighted average... The relative atomic mass is closer to 32 than to 34 because the isotope $^{32}S$ is much more abundant than the isotope $^{34}S$. [Explanation relating relative abundance to the weighted average]
How to earn full marks:
- State that $^{32}S$ is more abundant than $^{34}S$.
- Relate the higher abundance of $^{32}S$ to the relative atomic mass being closer to 32.
(c) (i)
- Each oxygen atom contributes 6 outer shell electrons... [Correct number of electrons on each oxygen]
- The sulfur atom contributes 6 outer shell electrons... [Correct number of electrons on the sulfur]
- There are two double bonds... [Correctly show the double bonds]
How to earn full marks:
- Correct number of electrons on each oxygen atom (6 outer shell).
- Correct number of electrons on the sulfur atom (6 outer shell).
- Correctly show the two double bonds between sulfur and each oxygen atom.
- Use different symbols (dots and crosses) to distinguish electrons from sulfur and oxygen.
(c) (ii)
Acid rain reacts with limestone... ...causing it to erode/dissolve. [State the effect of acid rain on limestone]
Limestone is calcium carbonate... ...and reacts with the acid in acid rain. [Explain the reaction with limestone]
How to earn full marks:
- State that acid rain causes erosion/dissolving of the limestone.
- Explain that limestone (calcium carbonate) reacts with the acid.
Common Pitfall: When drawing dot-and-cross diagrams, make sure you only show the outer shell electrons and that you clearly indicate which atom each electron comes from (using dots and crosses). Also, remember that acid rain erodes limestone because the acid reacts with the calcium carbonate in the limestone.