Isotopes

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.

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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:

1. Atom: $^{12}_{6}\text{C}$ has 6 protons and 6 neutrons ($12 - 6 = 6$).
2. Ion: $^{35}_{17}\text{Cl}^{-}$
   • Protons: 17
   • Neutrons: 18 ($35 - 17 = 18$)
   • Electrons: 18 (The "$-$" sign means it has gained one electron: $17 + 1 = 18$).

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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 $A_r$.

1. $(35 \times 75) = 2625$
2. $(37 \times 25) = 925$
3. $2625 + 925 = 3550$
4. $3550 / 100 = 35.5$ Answer: $A_r$ of $\text{Cl} = 35.5$

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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.

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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.

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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.