Discovery of Sub-atomic Particles

Cathode rays and the electron. Seal a glass tube at very low pressure, put electrodes at each end, and apply a high voltage. A glow travels from the cathode (negative electrode) toward the anode — these are cathode rays. J. J. Thomson's systematic study in 1897 showed three things: the rays travel in straight lines (they cast sharp shadows of objects in their path), they are bent by electric and magnetic fields toward the positive plate (proving negative charge), and — the decisive clue — the charge-to-mass ratio $e/m$ measured from that bending comes out to the same value no matter what gas fills the tube or what metal the electrodes are made of. A particle identical regardless of source material cannot be a property of one element; it must be a constituent of all matter. Thomson had found the electron. Thomson's measured value was $e/m = 1.76 \times 10^{11}\ \text{C kg}^{-1}$. That ratio alone cannot separate charge from mass, so a second experiment was needed. Robert Millikan's oil-drop experiment (1909) suspended charged oil droplets between charged plates and measured their charge directly, always finding it a whole-number multiple of $e = 1.6 \times 10^{-19}\ \text{C}$ — the electron's charge. Millikan did not discover the electron; he pinned down its charge with precision, a different and later achievement. Combining the two results gives the electron's mass:

where: $e$ is the electron's charge in coulombs, $e/m$ is Thomson's measured charge-to-mass ratio, and $m_e$ is the resulting electron mass in kilograms. This division is worked in full in the derivation block below.

Canal rays and the proton. In 1886 Eugen Goldstein used a cathode with holes drilled through it and noticed a second, fainter glow streaming through those holes, away from the anode side. These canal rays (anode rays) are deflected by fields away from the positive plate, showing positive charge. Unlike cathode rays, their $e/m$ ratio changes with the gas in the tube — because canal rays are not a universal particle but ionised atoms of the residual gas, each missing one or more electrons, and different gases have different masses. The lightest particle obtainable this way, from hydrogen gas, carries a charge of $+1.6\times10^{-19}\ \text{C}$ (equal and opposite to the electron's) and a mass of about $1.67\times10^{-27}\ \text{kg}$, roughly 1837 times heavier than the electron. This particle was named the proton, a fundamental constituent of every nucleus, unlike ordinary canal-ray ions (whole atoms missing electrons).

The neutron. By the early 1930s a problem was obvious: adding up the mass contributed by protons and electrons in an atom like helium did not account for its measured mass — electrons are too light to make up the difference, and the proton count (fixed by charge) was too small. Something with mass but no charge had to be present. James Chadwick confirmed this in 1932 by bombarding beryllium with alpha particles and detecting a highly penetrating, uncharged radiation that knocked protons out of paraffin wax with considerable energy — consistent only with a neutral particle of mass close to the proton's. This neutron has mass about $1.675\times10^{-27}\ \text{kg}$ and zero charge. With it, the mass-accounting problem disappeared: mass number now equals protons plus neutrons, matching measured atomic masses.

Naming the nucleus: $Z$, $A$, isotopes, isobars. Once all three particles are known, every atom can be described by two counting numbers. The atomic number $Z$ is the number of protons, which also equals the number of electrons in a neutral atom (zero net charge). The mass number $A$ is protons plus neutrons. A nuclide is written $^{A}_{Z}X$, with $A$ above and $Z$ below the symbol. Two atoms are isotopes if they share $Z$ (same element) but differ in $A$ — hydrogen's $^{1}_{1}H$, $^{2}_{1}H$, $^{3}_{1}H$ all have one proton but zero, one, and two neutrons. Two atoms are isobars if they share $A$ while belonging to different elements — $^{40}_{18}Ar$ and $^{40}_{20}Ca$ both have mass number 40, but argon has 22 neutrons and calcium has 20.

Question. An atom has 17 protons and 18 neutrons. Find its atomic number, mass number, and electron count if neutral, write its nuclide symbol, and state whether a second atom of the same element with 20 neutrons would be an isotope or an isobar of the first.

Step 1. The atomic number equals the proton count directly: $Z = 17$.

Step 2. The mass number is protons plus neutrons: $A = 17 + 18 = 35$. For a neutral atom electrons balance protons exactly, so electrons $= 17$.

Step 3. Assemble the nuclide symbol: $^{35}_{17}Cl$, chlorine-35 — atomic number 17 identifies the element as chlorine.

Step 4. A second chlorine atom (same $Z = 17$) with 20 neutrons instead of 18 has $A = 17 + 20 = 37$, giving $^{37}_{17}Cl$. Since both share $Z = 17$ but differ in $A$, they are isotopes, not isobars — this pair is exactly the natural chlorine mixture responsible for chlorine's non-integer average atomic mass on the periodic table.

Final answer: $Z = 17$, $A = 35$, 17 electrons, symbol $^{35}_{17}Cl$; the 37-neutron variant is an isotope of it, $^{37}_{17}Cl$.

Competitive stretch

Two atoms X and Y both have mass number 14; X has $Z = 6$, Y has $Z = 7$. For X, neutrons $= 14 - 6 = 8$, giving carbon-14, $^{14}_{6}C$. For Y, neutrons $= 14 - 7 = 7$, giving nitrogen-14, $^{14}_{7}N$. Since X and Y share $A$ but differ in $Z$, they are isobars, not isotopes — a useful check that the two classifications are opposites, not synonyms.

• Mixing up isotopes and isobars: isotopes share the same atomic number $Z$ (same element, different neutron count); isobars share the same mass number $A$ (different elements that happen to weigh the same).
• Reversing the direction cathode rays bend in a field — they deflect toward the positive plate because they are negatively charged, not away from it.
• Treating canal-ray $e/m$ as a universal constant the way cathode-ray $e/m$ is. It is not: canal rays are ionised leftover gas atoms, so $e/m$ depends on the gas in the tube.
• Crediting Millikan with discovering the electron. Thomson discovered the particle itself (1897); Millikan's later oil-drop work (1909) only measured its charge precisely.
• Forgetting that mass number counts protons and neutrons together — a common slip is writing $A = Z$ when a question gives neutron count separately.

Ask the tutor: if you would like to work through why the electron-mass division in the derivation gives 9.1 and not some other figure, or practice more $Z$, $A$, isotope, and isobar problems, ask the AI tutor to walk through a few with you.