Atomic Structure and Isotopes (4E) - MCAT Chemical and Physical Foundations of Biological Systems

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

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

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

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.

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.

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

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 $Z$.

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

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.

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

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

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

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

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

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

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

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

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

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

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

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 $f_i$.

$1\ \text{amu} = \frac{1}{12}$ 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.

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.