Atomic Structure and Isotopes (4E) - Chem & Physics

1. What is the definition of isotopes of the same element?

   Same $Z$ (protons), different $A$ (neutrons). Isotopes share the same atomic number $Z$ but differ in mass number $A$ due to varying neutron counts.

2. Identify the formula for neutrons $n$ in terms of mass number $A$ and atomic number $Z$.

   $n = A - Z$. Subtracting atomic number $Z$ from mass number $A$ yields the neutron count, as $A$ includes both protons and neutrons.

3. State the formula for the average atomic mass from isotopic masses and fractional abundances.

   Average mass $= \sum_i (m_i \times f_i)$. Average atomic mass is the weighted sum of each isotope's mass $m_i$ multiplied by its fractional abundance $f_i$.

4. Find the number of neutrons in $^{37}_{17}\text{Cl}$.

   $20$ neutrons. Neutron number is calculated as mass number minus atomic number: $37 - 17 = 20$.

5. What quantity does mass number $A$ represent for a nuclide?

   Total nucleons: $A = p + n$. The mass number $A$ equals the sum of protons and neutrons, representing the total number of nucleons in the nucleus.

6. Find the number of electrons in $^{56}_{26}\text{Fe}^{3+}$.

   $23$ electrons. The +3 charge indicates loss of 3 electrons from neutral iron's 26, leaving 23 electrons.

7. Find the number of protons, neutrons, and electrons in neutral $^{23}_{11}\text{Na}$.

   $p=11$, $n=12$, $e=11$. For neutral sodium, protons equal $Z=11$, neutrons are $23-11=12$, and electrons match protons.

8. Calculate average atomic mass for $^{35}\text{Cl}$ at $75\%$ and $^{37}\text{Cl}$ at $25\%$.

   $35.5\ \text{amu}$. Weighted average: $0.75 \times 35 + 0.25 \times 37 = 26.25 + 9.25 = 35.5$ amu.

9. What is the charge (in units of $e$) and approximate location of an electron in an atom?

   Charge $-1e$; located outside the nucleus. Electrons possess a negative charge equal to the elementary charge and occupy orbitals in the electron cloud surrounding the nucleus.

10. Identify the number of electrons in a neutral atom with atomic number $Z$.

    Electrons $= Z$. In neutral atoms, electron count equals the atomic number $Z$ to balance the positive charge from protons.

11. What is the approximate relative mass of a neutron compared with a proton?

    Neutron mass is approximately equal to proton mass. Neutrons and protons have nearly identical masses, both contributing significantly to atomic mass.

12. Which subatomic particle primarily changes between isotopes of the same element?

    Neutrons. Isotopes vary in neutron number while maintaining the same proton count, affecting mass but not chemical identity.

13. State the relationship between net ionic charge, protons $p$, and electrons $e$.

    Net charge $= p - e$ (in units of $e$). Net charge arises from the difference between positively charged protons and negatively charged electrons.

14. What is the charge (in units of $e$) and approximate location of a neutron in an atom?

    Charge $0$; located in the nucleus. Neutrons have no net charge and contribute to the nuclear mass while stabilizing the nucleus against proton repulsion.

15. What is the definition of atomic mass unit in terms of $^{12}\text{C}$?

    $1\ \text{amu} = \frac{1}{12}$ the mass of one $^{12}\text{C}$ atom. The amu is defined relative to carbon-12, where 1 amu equals one-twelfth its atomic mass.

16. Which subatomic particle primarily determines an element's chemical identity?

    Protons (atomic number $Z$). The number of protons determines the element's position in the periodic table and its chemical behavior.

17. What does the notation $^{A}_{Z}X$ specify about an atom or ion?

    Element $X$, with mass $A$ and atomic number $Z$. Nuclide notation $^{A}_{Z}X$ indicates the element symbol $X$ with its specific mass number $A$ and atomic number $Z$.

18. Which option best describes an anion: loss of electrons or gain of electrons?

    Gain of electrons. Anions are negatively charged ions formed by gaining electrons, increasing electron count above protons.

19. What is the definition of an ion in terms of electrons and protons?

    Species with $e^- \neq p^+$ (net charge not zero). An ion forms when the number of electrons differs from protons, resulting in a nonzero net charge.

20. What is the approximate relative mass of a proton compared with an electron?

    Proton is about $1836\times$ the electron mass. Protons are much heavier than electrons, with a mass ratio of approximately 1836:1.

21. What is the charge (in units of $e$) and approximate location of a proton in an atom?

    Charge $+1e$; located in the nucleus. Protons carry a positive charge equal to the elementary charge and form part of the dense central nucleus along with neutrons.

22. What quantity does atomic number $Z$ represent for an element?

    Number of protons in the nucleus. The atomic number $Z$ defines the element's identity by specifying the number of protons, which determines its chemical properties.

23. Which option best describes a cation: loss of electrons or gain of electrons?

    Loss of electrons. Cations are positively charged ions formed by losing electrons, reducing electron count below protons.

24. Find the net charge (in units of $e$) for a species with $p=16$ and $e=18$.

    Net charge $=-2$. Net charge is protons minus electrons: $16 - 18 = -2$, indicating an anion.

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