What is an isotope? For any given element, it is an atom with which of the following?
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A
a different atomic number
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B
a different number of protons
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C
a different number of electrons
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D
a different mass number
Isotopes are atoms of the same element possessing identical atomic numbers (proton counts) but different mass numbers due to varying neutron counts within the nucleus.
Isotopes maintain identical chemical properties because electron configuration and thus chemical behavior—depends solely on proton number, while differing in nuclear mass and stability due to neutron number variations that affect nuclear binding energy without altering elemental identity.
A) a different atomic number
Atomic number defines elemental identity as the count of protons in the nucleus; changing this value transforms the atom into a different element entirely. Carbon (atomic number 6) becomes nitrogen (atomic number 7) upon gaining a proton—not an isotope but a transmutation. Isotopes by definition preserve atomic number while varying only in neutron content, making different atomic numbers incompatible with isotopic relationships.
B) a different number of protons
Proton count determines an atom's position in the periodic table and its fundamental chemical nature. All carbon atoms contain exactly six protons; atoms with five protons are boron, seven protons are nitrogen. Isotopes of carbon (¹²C, ¹³C, ¹⁴C) all possess six protons—differing only in neutrons (6, 7, and 8 respectively). Altering proton number changes elemental identity rather than creating isotopic variants, violating the definition of isotopes as variants within a single element.
C) a different number of electrons
Electron count variations produce ions (charged species), not isotopes. A neutral carbon atom has six electrons; losing electrons creates C⁺ or C²⁺ cations, gaining electrons forms C⁻ anions—but all remain carbon isotopes if proton count stays six. Isotopes specifically describe nuclear composition differences (neutron count), independent of electron configuration which determines charge state but not isotopic identity. Carbon-12 atoms can exist as neutral atoms, cations, or anions while remaining ¹²C isotopes.
D) a different mass number
Mass number (sum of protons and neutrons) varies among isotopes while proton count remains constant. Carbon-12 (6 protons + 6 neutrons, mass number 12), carbon-13 (6 protons + 7 neutrons, mass number 13), and carbon-14 (6 protons + 8 neutrons, mass number 14) exemplify isotopic variation—all chemically carbon but differing in nuclear mass and stability (¹⁴C is radioactive while ¹²C and ¹³C are stable). This mass variation enables isotopic applications: ¹³C in metabolic tracing via mass spectrometry, ¹⁴C in radiocarbon dating, and ²H (deuterium) in NMR spectroscopy—all leveraging identical chemistry with detectable mass differences.
Conclusion:
Isotopes represent nuclear variants of a single element distinguished solely by neutron count, reflected in different mass numbers while maintaining identical atomic numbers. This definition preserves chemical identity (governed by proton-electron relationships) while allowing nuclear property variations affecting mass, density, vibrational frequencies, and nuclear stability. Options A and B describe elemental transmutation rather than isotopic variation, while option C describes ionization states. Only option D correctly identifies mass number variation—the measurable consequence of differing neutron counts that defines isotopic relationships without altering chemical behavior. Understanding isotopes proves essential for radiometric dating, medical imaging (e.g., ¹⁸F-PET scans), metabolic research, and nuclear energy applications.