Lecture Notes: Atomic Number, Mass Number, and Isotopes

Atomic Number, Mass Number, and Isotopes

• Atomic number (symbol: $Z$)

  • Represents the number of protons in the nucleus.

  • For a neutral atom, the number of electrons equals the number of protons, so $E = Z$ for a neutral atom.

  • Potassium (K): $Z = 19$; Phosphorus (P): $Z = 15$.

  • In the periodic table, the whole number above the element symbol is the atomic number. Therefore, potassium has 19 protons, phosphorus has 15 protons.

  • Statement from lecture: "All potassium atoms will have 19 protons, and all phosphorus atoms will have 15 protons. Since atoms are neutral, for every positive proton, there’s a negative electron. So potassium would also have 19 electrons, and phosphorus would have 15 electrons."

• Mass number (symbol: $A$)

  • Represents the total number of protons and neutrons in the nucleus: $A = Z + N$, where $N$ is the number of neutrons.

  • The particles that contribute to the mass number (protons and neutrons) are located in the nucleus.

  • Important distinction: The mass number is not shown on the periodic table. The numbers beneath the symbols on the periodic table (with decimals) are atomic mass, not the mass number.

  • The lecture emphasizes: "The mass number is not on the periodic table" and that the decimals under the symbols are atomic mass (average mass), not the mass number.

  • Notation for isotopes often uses: $^{A}_{Z}X$, where $X$ is the symbol of the element, $A$ is the mass number, and $Z$ is the atomic number (number of protons).

  • Sometimes the $Z$ is omitted because you can read it from the element symbol in the periodic table.

  • Formula relationships:

  • $A = Z + N$

  • $N = A - Z$

• Isotopes: same element, different neutrons

  • Definition: isotopes are atoms with the same number of protons (same $Z$) but different numbers of neutrons (different $N$, hence different $A$).

  • Key point from lecture: "Isotopes are atoms with the same number of protons but different number of neutrons."

  • Examples from the lecture:

  • Copper isotopes: $Z = 29$.

    • $^{63}_{29} ext{Cu}$: $A = 63$; neutrons $N = A - Z = 63 - 29 = 34$; electrons in a neutral atom: $E = Z = 29$.

    • $^{65}_{29} ext{Cu}$: $A = 65$; neutrons $N = 65 - 29 = 36$; electrons $E = 29$ (neutral).

    • Conclusion: These two copper species are isotopes of copper.

  • Tin isotope example: $Z = 50$, $A = 121$.

    • Neutrons $N = A - Z = 121 - 50 = 71$; electrons for a neutral tin atom: $E = Z = 50$.

    • Tin with charge +2: Since the charge is +2, electrons would be $E = Z - 2 = 50 - 2 = 48$; neutrons remain $N = 71$; mass number remains $A = 121$.

    • Note from transcript: Tin-121 is not an isotope of copper (different $Z$).

  • Sodium isotopes discussed in the chart:

    • Sodium: $Z = 11$.

    • Example with neutral sodium: $A = 23$ → $N = A - Z = 23 - 11 = 12$; electrons $E = 11$; charge 0.

    • Another example in the transcript: a sodium example with $A = 35$ and charge +1 (cation).

    • For a charged species with $+1$, $E = Z - 1 = 11 - 1 = 10$; neutrons $N = A - Z = 35 - 11 = 24$; overall charge is +1.

    • The lecture also notes an attempt to identify isotopes of sodium: the two isotopes mentioned are sodium-23 and sodium-36 (i.e., $^{23}<em>{11} ext{Na}$ and $^{36}</em>{11} ext{Na}$) according to the example.

• Notation and notional examples clarified

  • Isotopic notation: $^{A}_{Z}X$ (mass number on top, atomic number on bottom, element symbol to the right).

  • Sometimes the notation appears without the protons (the $Z$) if the element is clear from context (you know the element from the symbol).

  • The mass number $A$ is distinct from the atomic mass shown on the periodic table (which is typically a decimal value representing the weighted average of isotopes).

  • The mass number is always an integer; the atomic mass on the table is not the same thing as the mass number.

• Practice calculations to reinforce concepts

  • Example 1: Bromine

  • Element: Br; $Z = 35$; neutral so $E = 35$.

  • Mass number given: $A = 80$; Neutrons $N = A - Z = 80 - 35 = 45$.

  • Result: $^{80}_{35} ext{Br}$ (neutral).

  • Example 2: Sodium (first chart entry)

  • Element: Na; $Z = 11$; neutral so $E = 11$.

  • Mass number: $A = 23$; Neutrons $N = 23 - 11 = 12$.

  • Result: $^{23}_{11} ext{Na}$ (neutral).

  • Example 3: Sodium with a +1 charge (using the chart’s last line)

  • Given: $Z = 11$; charge = +1, so $E = Z - 1 = 10$.

  • Mass number: $A = 35$; Neutrons $N = A - Z = 35 - 11 = 24$.

  • Result: $^{35}_{11} ext{Na}^{+}$ with $E = 10, N = 24$.

  • Note on arithmetic accuracy: The lecture transcript shows an inconsistency when calculating the neutrons for the Na example with $A = 35$ and Z = 11 (one line shows 25 neutrons and another shows 24). The correct neutron count is $N = A - Z = 35 - 11 = 24<br>ight.$.

• Quick recap: key takeaways

  • Atomic number $Z$ uniquely identifies an element; determines protons and, for neutral atoms, electrons.

  • Mass number $A$ is the sum of protons and neutrons; it is not shown on the periodic table; it is used to describe isotopes.

  • Isotopes have the same $Z$ but different $A$ (hence different $N$).

  • The periodic table provides atomic mass (a decimal) below symbols, which is not the same as the integer mass number $A$.

  • Ion charge is determined by the difference between protons and electrons: charge = $Z - E$. Neutral atoms have charge 0; cations have positive charge; anions have negative charge.

• Connections to foundational principles and real-world relevance

  • The concept of isotopes arises from the fact that nuclei can contain varying numbers of neutrons without changing the identity of the element (same $Z$, different $A$).

  • In chemistry and physics, isotopes explain variations in mass but similar chemical behavior (due to the same electron configuration given by $Z$).

  • Isotopes have practical applications (e.g., medical imaging, radiometric dating, and research) and also require ethical and safety considerations when using radioactive species. This lecture lays the groundwork for distinguishing isotopes and understanding their properties based on protons, neutrons, and electrons.

• Summary of symbols and formulas to memorize

  • Protons: $P = Z$

  • Electrons (neutral): $E = Z$

  • Neutrons: $N = A - Z$

  • Mass number relation: $A = Z + N$

  • Ion charge: $ext{charge} = Z - E$

  • Isotope notation: $^{A}_{Z}X$

  • Important distinction: $A$ (mass number) vs. atomic mass (on the periodic table, decimal) – they are not the same.