Atomic Structure and Isotopes (4E)
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MCAT Chemical and Physical Foundations of Biological Systems › Atomic Structure and Isotopes (4E)
In a metabolic tracing study, a researcher combusts purified glucose isolated from cells fed a mixture of $^{12}\text{CO}_2$ and $^{13}\text{CO}_2$. The CO$_2$ produced from combustion is analyzed by mass spectrometry, yielding two dominant peaks at 44.0 amu (assigned to $^{12}\text{C}^{16}\text{O}_2$) and 45.0 amu (assigned to $^{13}\text{C}^{16}\text{O}_2$). If the 45.0 amu peak has 25% of the intensity of the 44.0 amu peak, which statement about the carbon isotopes in the original glucose is most consistent with these results? (Use: $m(^{12}\text{C})=12.000$ amu, $m(^{13}\text{C})=13.003$ amu, $m(^{16}\text{O})=15.995$ amu.)
The glucose must contain 25% more total carbon atoms when labeled with $^{13}\text{C}$ due to the higher atomic mass.
Approximately 25% of the carbon atoms in the glucose are $^{13}\text{C}$ because peak intensity equals isotope fraction directly.
Approximately 20% of the carbon atoms in the glucose are $^{13}\text{C}$, assuming similar ionization/detection for the two isotopologues.
The glucose contains the same fraction of $^{13}\text{C}$ as $^{12}\text{C}$ because isotopes are chemically indistinguishable.
Explanation
This question tests understanding of atomic structure and isotopic behavior, focusing on isotope abundance calculations from mass spectrometry data. Isotopes are variants of a chemical element that differ in neutron number, and their relative abundances can be determined from mass spectrometry peak intensities. In this scenario, glucose combustion produces CO₂ molecules containing either ¹²C or ¹³C, with the 45.0 amu peak (¹³CO₂) showing 25% of the intensity of the 44.0 amu peak (¹²CO₂). Choice A is correct because when each CO₂ molecule contains one carbon atom, a 25% relative intensity means that for every 100 carbon atoms, approximately 20 are ¹³C (20/(20+80) = 0.20 or 20%). Choice B is incorrect because it confuses relative intensity (25% of the ¹²C peak) with absolute fraction (which would be 20%, not 25%). To avoid similar errors, remember that relative peak intensity must be converted to fractional abundance using the formula: fraction = relative intensity/(1 + relative intensity).
In a tracer study of glucose metabolism, a researcher compares two isotopes: $^{14}\mathrm{C}$ (6 protons, 8 neutrons) and $^{14}\mathrm{N}$ (7 protons, 7 neutrons). Which statement about these two nuclides is most consistent with atomic-structure principles?
They are isotopes of the same element because they have the same mass number.
They must have identical chemical reactivity because their mass numbers are equal.
They are isobars because they have the same mass number but different atomic numbers.
They are isomers because they have the same number of neutrons.
Explanation
This question tests understanding of atomic structure and isotopic behavior, focusing on the classification of nuclides with identical mass numbers. Isobars are nuclides that have the same mass number (A = protons + neutrons) but different atomic numbers (different numbers of protons), making them different elements entirely. In this scenario, both ¹⁴C (6 protons + 8 neutrons = 14) and ¹⁴N (7 protons + 7 neutrons = 14) have mass number 14 but different atomic numbers. Choice C is correct because it accurately identifies these nuclides as isobars with the same mass number but different atomic numbers. Choice A is incorrect because isotopes must have the same number of protons, not just the same mass number. To avoid confusion, remember that isotopes share the same element (same protons), while isobars share the same mass number but are different elements.
A sample contains only two isotopes of lithium: $^{6}\text{Li}$ (6.02 amu) and $^{7}\text{Li}$ (7.02 amu). The measured average atomic mass is 6.94 amu. Which statement about isotopic abundance is most consistent with this result?
$^{7}\text{Li}$ is more abundant than $^{6}\text{Li}$
$^{6}\text{Li}$ is more abundant than $^{7}\text{Li}$
Both isotopes must be present in equal abundance
Average atomic mass depends only on proton number, so abundance cannot be inferred
Explanation
This question tests understanding of atomic structure and isotopic behavior, focusing on abundance inference from average mass. Isotopes are variants of a chemical element that differ in neutron number, and average mass reflects their proportional contributions. In this scenario, lithium's average is 6.94 amu, with isotopes at 6.02 and 7.02 amu. Choice B is correct because the average is closer to 7.02 amu, suggesting higher abundance of ^{7}Li. Choice C is incorrect because equal abundance would average to 6.52 amu, not 6.94 amu. To avoid similar errors, perform weighted average calculations for precision. Always base inferences on data rather than assumptions of equality.
In an isotopic labeling experiment, glucose is synthesized using water enriched in deuterium ($^2\text{H}$). Compared with protium ($^1\text{H}$), deuterium differs primarily in which subatomic particle count?
One additional proton
One additional positron in the nucleus
One additional neutron
One additional electron in a neutral atom
Explanation
This question tests understanding of atomic structure and isotopic behavior, focusing on subatomic differences between isotopes. Isotopes are variants of a chemical element that differ in neutron number, affecting mass but not charge or electron count in neutral atoms. In this scenario, deuterium $(^2H$) is compared to protium $(^1H$) in a labeling experiment. Choice A is correct because deuterium has one more neutron, increasing its mass by approximately 1 amu. Choice C is incorrect because neutral atoms of hydrogen isotopes both have one electron. To avoid similar errors, focus on nuclear composition for isotopic differences. Always recall that electrons are determined by atomic number, not mass.
A lab identifies an ion as $^{35}\text{Cl}^-$. Which statement is most consistent with this notation?
It has 18 protons and 17 electrons
It has 17 protons and 18 electrons
It has 35 neutrons and 17 protons
It has 35 protons and 35 electrons
Explanation
This question tests understanding of atomic structure and isotopic behavior, focusing on interpreting ion notation. Isotopes are variants of a chemical element that differ in neutron number, and ion notation includes charge affecting electron count. In this scenario, the ion is ^{35}Cl^-. Choice B is correct because chlorine has 17 protons, and the negative charge adds one electron for 18 electrons. Choice D is incorrect because it confuses neutrons with the mass number minus protons (18 neutrons), but misses electron count. To avoid similar errors, subtract atomic number from mass number for neutrons. Always account for charge when determining electron numbers in ions.
A lab reports that an unknown element X has two isotopes, $^{62}\text{X}$ and $^{64}\text{X}$, and the average atomic mass is 63.60 amu. Which isotope is most abundant?
$^{63}\text{X}$, because average atomic mass must match an existing isotope
$^{62}\text{X}$, because it is lighter and thus contributes more strongly to the average
$^{64}\text{X}$, because the average is closer to 64 than to 62
Both are equally abundant because the average is between them
Explanation
This question tests understanding of atomic structure and isotopic behavior, focusing on abundance from average mass. Isotopes are variants of a chemical element that differ in neutron number, influencing the weighted average mass. In this scenario, element X has average mass 63.60 amu with isotopes at 62 and 64. Choice C is correct because 63.60 is closer to 64, indicating higher abundance of ^{64}X. Choice D is incorrect because equal abundance would average to 63, not 63.60. To avoid similar errors, use the formula for weighted averages to estimate ratios. Always verify by calculating the deviation from the midpoint.
A biochemist uses $^{15}\text{N}$-labeled ammonium to track incorporation into nucleotides. Compared with $^{14}\text{N}$, the $^{15}\text{N}$ nucleus has which change?
One additional proton; the neutron number is unchanged
A different number of protons, making it a different element
One additional neutron; the atomic number is unchanged
One fewer electron in the neutral atom
Explanation
This question tests understanding of atomic structure and isotopic behavior, focusing on nuclear changes in isotopes. Isotopes are variants of a chemical element that differ in neutron number, preserving the atomic number. In this scenario, ^{15}N is compared to ^{14}N in nucleotide labeling. Choice A is correct because ^{15}N has one more neutron, with unchanged atomic number 7. Choice D is incorrect because different proton counts define different elements, not isotopes. To avoid similar errors, confirm atomic number consistency for isotopes. Always note that electron counts in neutral atoms are tied to protons, not neutrons.
A researcher analyzes nitrogen isotopes in amino acids and considers $^{14}\text{N}$ and $^{15}\text{N}$. If both atoms are neutral, which statement is true?
They have different atomic numbers but the same mass number
They have the same number of electrons and different numbers of neutrons
They have identical neutron numbers but different proton numbers
They have different numbers of electrons because mass number differs
Explanation
This question tests understanding of atomic structure and isotopic behavior, focusing on electron and neutron counts in neutral isotopes. Isotopes are variants of a chemical element that differ in neutron number, but neutral atoms of the same element have the same electron count equal to the atomic number. In this scenario, neutral ^{14}N and ^{15}N atoms are analyzed for their subatomic particles. Choice A is correct because both have 7 electrons (atomic number of nitrogen) but differ in neutrons. Choice B is incorrect because electron count in neutral atoms depends on protons, not mass number. To avoid similar errors, recall that atomic number determines electron count in neutral atoms. Always differentiate between nuclear composition and electronic structure.
A chemist calculates an element’s average atomic mass as 10.81 amu from a natural sample. The element has two stable isotopes: $^{10}\text{B}$ (10.01 amu) and $^{11}\text{B}$ (11.01 amu). Based on the average mass, which isotope is most abundant?
They must be 50/50 because the average lies between 10 and 11
$^{10}\text{B}$, because it has the smaller mass and thus dominates the average
Neither; average atomic mass equals the mass number of the most stable isotope
$^{11}\text{B}$, because the average is closer to 11.01 amu
Explanation
This question tests understanding of atomic structure and isotopic behavior, focusing on determining abundance from average atomic mass. Isotopes are variants of a chemical element that differ in neutron number, and average mass is weighted by their natural abundances. In this scenario, boron's average mass is 10.81 amu, with isotopes at 10.01 and 11.01 amu. Choice B is correct because the average is closer to 11.01 amu, indicating higher abundance of ^{11}B. Choice C is incorrect because a 50/50 ratio would yield an average of 10.51 amu, not 10.81 amu. To avoid similar errors, use the weighted average formula to quantify abundances. Always compare the average to isotopic masses to infer dominance.
A radiochemistry technician compares $^{12}\text{C}$ and $^{14}\text{C}$ in a sample of labeled urea. Which statement about these two atoms is true?
They have the same number of protons but different numbers of neutrons
They differ in the number of valence electrons in the neutral atom
They have different atomic numbers, so they are different elements
They are isotopic isomers that differ in bond angles
Explanation
This question tests understanding of atomic structure and isotopic behavior, focusing on fundamental differences between isotopes. Isotopes are variants of a chemical element that differ in neutron number, maintaining the same proton count. In this scenario, ^{12}C and ^{14}C are compared in labeled urea. Choice B is correct because both have 6 protons but differ by 2 neutrons. Choice A is incorrect because same atomic number means they are the same element. To avoid similar errors, check atomic numbers for elemental identity. Always distinguish isotopes from ions or isomers in comparisons.