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The atomic number $Z$ is the number of protons in an atomic nucleus, and fixes the chemical element. It is a count, with no units. An atomic nucleus with six protons is always carbon, regardless of how many neutrons accompany them or how many Electrons surround it. See the IUPAC Gold Book, atomic number.

Three independent bookkeeping questions become easy once their symbols are kept separate. Let $N$ count neutrons, $n_e$ count Electrons, $A$ be the mass number, and $Q$ be the net electric charge. A proton carries electric charge $+e$ and an Electron carries $-e$, where $e$ is the positive elementary charge; a neutron carries zero net electric charge. HenceThe reasoning is just counting: add protons and neutrons for $A$, and subtract negative Electron contributions from positive proton contributions for $Q$. A neutral chemical atom has $Q=0$, so $n_e=Z$. For a positively charged ion, fewer Electrons remain. Notation ${}_Z^A\mathrm{X}$ gives the mass number at upper left and atomic number at lower left, with $\mathrm{X}$ standing for the chemical element; a right superscript such as $+$ specifies the electric charge in units of $e$. See Flowers et al., Chemistry 2e, atomic structure and symbolism.

For neutral carbon-12, ${}_6^{12}\mathrm{C}$, the atomic number gives six protons, the subtraction $N=12-6=6$ gives six neutrons, and neutrality gives six Electrons. Neutral carbon-13, ${}_6^{13}\mathrm{C}$, instead has $N=13-6=7$ neutrons, with the same six protons and six Electrons. Thus these two isotopes occupy the same carbon box in the periodic table.

For neutral sodium of mass number $23$, ${}_{11}^{23}\mathrm{Na}$, the counts are eleven protons, $23-11=12$ neutrons, and eleven Electrons. Removing one Electron gives the ion ${}_{11}^{23}{\mathrm{Na}}^{+}$: $Q/e=1$, so $n_e=11-1=10$. Both its atomic number and its twelve neutrons stay unchanged. This is ionization, not conversion into the chemical element neon, even though a neutral neon chemical atom also has ten Electrons.

This bookkeeping is useful whenever a symbol must be translated into a physical inventory. Mass number answers how many protons plus neutrons there are; electric charge answers the imbalance between protons and Electrons; atomic number alone answers which chemical element it is. Keeping those questions distinct prevents an isotope or an ion from being mistaken for a different chemical element.

The carbon isotope with six protons and seven neutrons. A neutral carbon-13 chemical atom has six Electrons.

A chemical element is an identity shared by all chemical atoms whose atomic nuclei contain the same number of protons. That number is its atomic number, $Z$: six means carbon, eleven means sodium. The identity survives differences in neutron count, which distinguish isotopes, and differences in Electron count, which distinguish neutral chemical atoms from ions. See the IUPAC Gold Book, chemical element.

The same name can also denote a pure chemical substance containing only that chemical element. These two uses answer different questions. Molecular oxygen, ${\mathrm{O}}_2$, is a chemical substance made entirely of oxygen; water, ${\mathrm{H}}_2\mathrm{O}$, is a chemical compound containing both hydrogen and oxygen. A water molecule contains three chemical atoms but only two chemical elements. Joining chemical atoms through chemical bonds changes their arrangement without changing their atomic numbers.

This distinction makes stoichiometry possible: ordinary chemical reactions rearrange chemical atoms, so one can count each chemical element before and after a transformation. Changing the proton count instead changes the chemical element and requires a nuclear reaction. The periodic table organizes these identities into a useful map, while atomic number bookkeeping keeps identity, isotope, and electric charge separate.

DNA replication copies a double-stranded DNA molecule into two daughter double-stranded DNA molecules. In semiconservative replication, each daughter retains one parental strand and receives one newly synthesized complementary strand. DNA polymerases build the new strands from incoming nucleotides; they do not make RNA or proteins in this copying step. See Alberts et al., Molecular Biology of the Cell, 4th edition (2002): DNA replication mechanisms.

For a five-base pair example, separate $5^{\prime }\text{-}\mathrm{ATGCC}\text{-}{3}^{\prime }$ from its partner $3^{\prime }\text{-}\mathrm{TACGG}\text{-}{5}^{\prime }$. Base pairing specifies a new TACGG partner for the old ATGCC strand and a new ATGCC partner for the old TACGG strand. With error-free copying, both daughter DNA molecules have the original nucleotide sequence, but different physical strand histories. One initial duplex contains ten nucleotides; one complete round produces two duplexes containing twenty nucleotides, ten retained and ten newly incorporated.

This is useful for inheritance: both daughter biological cells can receive a copy of the DNA record. The elegant feature is that base pairing lets each strand specify its missing partner. Direction matters too: a replicating DNA polymerase reads its template $3^{\prime }\to 5^{\prime }$ and extends the new strand at its $3^{\prime }$ end, so synthesis proceeds $5^{\prime }\to 3^{\prime }$. These are opposite directions on antiparallel nucleic acid strands, not two alternative directions of synthesis. The enzyme needs a pre-existing paired strand end to extend; the diagram omits the machinery that starts and coordinates copying. See Alberts et al.: template-directed synthesis and the requirement for a primer.

The strand accounting predicts observable differences between copying mechanisms. In 1958, Meselson and Stahl grew Escherichia coli with the heavier nitrogen isotope ${}^{15}\mathrm{N}$, then supplied ${}^{14}\mathrm{N}$ and measured extracted DNA by density-gradient centrifugation. After one generation their samples contained intermediate-density DNA; after two, intermediate-density and light DNA occurred in equal amounts. This supported semiconservative replication in the tested Escherichia coli culture. It was an isotope assay of sampled DNA, not simultaneous testing of every kind of DNA or direct colored-strand photography. See The replication of DNA in Escherichia coli by Matthew Meselson and Franklin W. Stahl.

In isopycnic centrifugation, a species concentrates near the position where the liquid's density matches its buoyant density. In a density gradient increasing outward, material displaced inward encounters less-dense liquid and tends to move outward; material displaced outward encounters denser liquid and tends to move inward. Diffusion broadens the resulting band. If the density gradient never reaches the species' buoyant density, a matching equilibrium position need not exist within the vessel.^[ref]

The 1958 paper The replication of DNA in Escherichia coli by Matthew Meselson and Franklin W. Stahl (pp. 672–676, Figures 1–4) makes the distinction concrete. Its separation apparatus was a Spinco Model E ultracentrifuge with an Escherichia coli lysate in a cesium chloride density gradient. Ultraviolet wave absorption photographs of the rotating sample were scanned with a recording microdensitometer: peak position reported buoyant density, while signal above baseline reported DNA concentration.^[ref]

Mixed lysates labeled fully with the nitrogen isotope ${}^{15}\mathrm{N}$ and unlabeled lysates supplied reference bands; a mixture including intermediate material checked its position relative to those references. Figure 1 followed band formation over time, helping distinguish a migrating distribution from an approximately stationary one. These controls address resolution, calibration and approach to equilibrium. They do not make every ultraviolet-absorbing component identifiable as DNA, or turn a band into a direct image of individual strands. The DNA replication article develops the copying inference; here the key result is a separation by buoyant density, not a claim that heavier-labeled DNA is physically larger.^[ref]

Isotopes of a chemical element have the same atomic number $Z$, hence the same number of protons, but different neutron numbers $N$ and therefore different mass numbers $A=Z+N$. For example, every neon atomic nucleus contains ten protons: neon-20, neon-21, and neon-22 contain ten, eleven, and twelve neutrons, respectively. They occupy one chemical element box in the periodic table, rather than three boxes.

Three labels answer different questions. The chemical element fixes $Z$; the isotope specifies which neutron number accompanies that $Z$; the ion label specifies the net electric charge. Neutral ${}_{10}^{22}\mathrm{Ne}$ and the ion ${}_{10}^{22}{\mathrm{Ne}}^{+}$ both contain ten protons and twelve neutrons; they contain ten and nine Electrons, respectively. Ordinary ionization changes the Electron count, leaving the isotope unchanged. Changing the neutron number can change nuclear binding energy and the possibility of radioactive decay. Isotopic abundances can help distinguish material sources, while radioactive decay can additionally supply chronological information.

A mass spectrum makes the distinction experimentally visible: a single chemical element can give separate ion peaks at different mass-to-charge ratios. Its bulk atomic weight is a weighted mean governed by isotopic abundances, rather than the location of one compulsory peak. The historical mass spectrograph experiment and the synthetic neon mass spectrum below illustrate these complementary observations.

Mass resolving power compares a peak coordinate $x$ with a stated width or separation criterion $\Delta x$. With $\Delta x$ taken as full width at half maximum, a Gaussian function of standard deviation $\sigma$ hasAt the neon-20 coordinate in the synthetic mass spectrum, $\sigma =0.04$ gives $\Delta x\approx 0.0942$ and $R\approx 212$, while $\sigma =0.70$ gives $\Delta x\approx 1.648$ and $R\approx 12.1$. The width criterion and relative peak areas both matter when judging whether a small neighboring isotope can be distinguished. Mass resolution also differs from the accuracy of a calibrated peak position.

Mass spectrometry separates and detects ions according to mass-to-charge ratio. It can distinguish isotopes which belong to the same chemical element but have different atomic masses. The instrument measures ions: interpreting the result as a neutral atomic mass requires accounting for Electron removal and its ionization energy. For a singly positive ion in its ground state, $m_{+}=m_{\mathrm{a}}-m_e+I/c^2$, where $m_e$ is the Electron rest mass, $I$ is the ionization energy, and $c$ is the speed of light.

For a simple illustrative analyzer, positive ions of mass $m$ and electric charge $q=ze$ gain kinetic energy $qV=m{v}^2/2$ across an electric potential difference $V$ before entering a transverse uniform magnetic field $B$. The Lorentz force supplies centripetal acceleration, soAt fixed $V$ and $B$, the measured bending radius $r$ separates mass-to-charge ratios, not masses independently of electric charge. This ideal model assumes negligible initial kinetic energy and speeds small compared with the speed of light; the historical focusing mass spectrograph used the geometry described below.

A mass spectrum displays detected signal against mass-to-charge ratio. Peak positions identify candidate ions; peak areas give isotopic abundances only after the response and overlapping contributions have been accounted for.

Broadening can hide a weak component without changing its area in this ideal model. An actual mass spectrum can also contain molecular ions, different electric charge states, background, and unequal detection responses. A missing visible peak therefore cannot by itself prove the absence of an isotope. Conversely, a fractional atomic weight is a property of a population: there is no requirement for an ion peak at the weighted mean.

The ratio of an ion's mass to its electric charge; in SI it has units $kg/C$. A convenient numerical mass spectrum coordinate is $x=(m/\mathrm{u})/z$, with $q=ze$ and positive integer $z$ here. This $x$ is dimensionless. Doubling $z$ at fixed mass halves $x$, so the electric charge state must be identified before assigning an isotope.

A nuclear species specified by atomic number, mass number, and nuclear energy state. Isotopes compare nuclides with the same atomic number; changing only the nuclear energy state does not create a different isotope.