A full lesson: a cartoon movie to start, then how tiny and how heavy the nucleus is, the atomic mass unit, isotopes and average atomic mass, building a nucleus from protons and neutrons, how Chadwick found the neutron, NEET shortcuts, problems to solve yourself, and 12 MCQs.
If an atom were a 100 m cricket stadium, its nucleus would be a 1 cm marble on the pitch. That marble carries more than 99.9 % of the mass, and it is built from Z protons and N neutrons: A = Z + N.
Kabir and Meera are at the stadium for an IPL match. Meera, who loves physics, says: "Imagine this whole stadium is one atom. Where is the nucleus?" Kabir points at the pitch. "Right there," says Meera, "but it would only be the size of a marble. And that marble would weigh more than everything else in the stadium put together."
Try it at home: put a mustard seed (about 1 mm) on the floor in the middle of a room. If the seed were a nucleus, the atom around it would be about 10 m across (about 5 m from the seed to its edge), bigger than most rooms. Everything between the seed and the walls is the region where the electrons move. An atom is mostly empty space, but almost all of its mass sits in that seed.
"Tiny in size, huge in mass. Keep that picture. In this lesson we weigh the nucleus with a new unit, the u, and open it to count what is inside: protons and neutrons."
"Rutherford found the nucleus by firing alpha particles at gold foil. Most of them went straight through. What does that tell you?"
The atom is mostly empty. Only the very few alpha particles that came close to the tiny, heavy, positive nucleus were turned back. The nucleus is about 10⁴ times smaller in radius than the atom.
The nucleus holds all the positive charge and more than 99.9 % of the mass of the atom, yet its radius is only about 10⁻⁴ of the atom's radius. Drag the zoom slider (or the canvas) from the whole atom down to the nucleus. Then switch to the mass view.
Atom ≈ 10⁻¹⁰ m, nucleus ≈ 10⁻¹⁵ to 10⁻¹⁴ m.
Volume goes as R³, so (10⁻⁴)³ = 10⁻¹². The atom is mostly empty space.
An electron is about 1/1836 of a proton, so the electrons add only a few hundredths of a percent.
"Radius ten thousand times smaller, volume a million million times smaller, and still more than 99.9 percent of the mass. That is why nuclear matter is so dense, which we calculate in Lesson 2."
A carbon atom has a mass of about 1.99 × 10⁻²⁶ kg. Numbers like this are awkward, so atomic masses are expressed in the atomic mass unit (u): one twelfth of the mass of a carbon-12 atom (the neutral atom, electrons included). Slice the carbon atom, then put other atoms on the balance.
So the mass of a carbon-12 atom is exactly 12 u, by definition.
Use 1.66 × 10⁻²⁷ kg in problems. Mass in kg = (mass in u) × 1.66 × 10⁻²⁷.
They are close to whole numbers but not equal. Lesson 3 explains why (mass defect). Measured with a mass spectrometer.
"Remember 1 u is 1.66 times 10 to the minus 27 kilogram. Every mass defect and binding energy sum in this chapter starts from here."
"Why do we use the mass of the neutral carbon atom, electrons and all, and not just the carbon nucleus?"
Mass spectrometers measure ions and atoms, and the neutral atom is what we can weigh most precisely. In Lesson 3 you will see that using atomic masses makes the electron masses cancel neatly.
Atoms of one element can have different masses. These varieties are isotopes: same chemistry, different mass. The atomic mass printed in your periodic table is the abundance-weighted average over the isotopes. Slide the abundance and watch the seesaw balance at the average.
NCERT's example. Abundances are the percentages found in nature.
Here Σ pᵢ = 100 %, so M̄ = 0.754 × 34.98 + 0.246 × 36.98.
Closer to 34.98 because ³⁵Cl is three times more common. The plain mean (35.98 u) is wrong.
| Isotope of hydrogen | Nucleus | Mass (approx.) | Note |
|---|---|---|---|
| Hydrogen ¹H | 1 proton | 1.0078 u | 99.985 % of natural hydrogen |
| Deuterium ²H | 1 p + 1 n | 2.0141 u | 0.015 %, stable (heavy water D₂O) |
| Tritium ³H | 1 p + 2 n | 3.0160 u | unstable, not found in nature, made artificially |
"Average atomic mass is a weighted mean; it equals the plain mean only when the abundances are equal. The answer always lies closer to the isotope that is more common. Use that to check your answer in two seconds."
The nucleus of ordinary hydrogen is the proton. A nucleus contains Z protons and N neutrons; together they are the nucleons, and their total is the mass number A = Z + N. Add and remove nucleons, or pick a preset, and read the symbol.
| Particle | Charge | Mass | Where |
|---|---|---|---|
| Proton p | +e = +1.6 × 10⁻¹⁹ C | 1.00727 u = 1.6726 × 10⁻²⁷ kg | nucleus (Z of them) |
| Neutron n | 0 | 1.00866 u = 1.6749 × 10⁻²⁷ kg | nucleus (N of them) |
| Electron e⁻ | −e | 0.00055 u (≈ m_p / 1836) | outside the nucleus (Z in a neutral atom) |
A on top, Z below. Gold-197: Z = 79 protons, N = 197 − 79 = 118 neutrons.
Nuclear charge = +Ze. A neutral atom also has Z electrons, outside the nucleus.
¹H, ²H, ³H all have Z = 1. Their masses are about 1, 2 and 3 times the proton mass.
"Z decides the element, because Z protons need Z electrons, and electrons decide the chemistry. N only changes the mass. That is why isotopes behave the same in a test tube."
"Deuterium and tritium both have one proton. Why are they about two and three times heavier than ordinary hydrogen?"
The extra mass must come from neutral particles inside the nucleus. Deuterium has one neutron, tritium has two. The neutron, about as heavy as a proton, was found by Chadwick in 1932: Stage 6.
When beryllium is bombarded with alpha particles, it gives out a neutral radiation that can knock protons out of paraffin wax (and out of light nuclei such as helium, carbon and nitrogen). Was it gamma photons, the only neutral radiation known then? Pick the guess, change the mass of the neutral particle, and see which explanation works.
To give the protons the energy observed (about 5.7 MeV), a photon would need far more energy than the alpha–beryllium reaction could supply.
Equal masses share energy best in a head-on hit. Comparing recoils of hydrogen and nitrogen gave a mass very close to the proton's.
A free neutron is unstable and decays into a proton, an electron and an antineutrino. Inside a nucleus it is stable.
"A neutral particle is invisible to electric fields, so Chadwick caught it by what it knocked out. Ball hits ball: equal masses pass on all the energy. That is how a carrom striker works too."
For an ion of charge q (in units of e). ³⁵₁₇Cl⁻: p = 17, n = 18, e = 18.
And N_A × 1 u = 6.022 × 10²³ × 1.66 × 10⁻²⁷ kg ≈ 1 g. That is why A u per atom means A g per mole.
Two isotopes: M̄ = m₁ + p₂(m₂ − m₁). Reverse: p₂ = (M̄ − m₁)/(m₂ − m₁).
Cube the radius ratio for volume. Atom 10⁻¹⁰ m, nucleus ~10⁻¹⁴ m.
1.00866 u > 1.00727 u; m_p ≈ 1836 m_e. ¹H atom = 1.007825 u (proton + electron).
Equal masses: 1 (all the energy). Neutron on nitrogen (M = 14): 56/225 ≈ 0.25.
"NEET loves counting questions: protons, neutrons, electrons in an ion. Write p, n, e in three columns before you look at the options, and you will never fall for the trap."
Cover the solution, write the formula, and solve on paper. Open the hint only if you are stuck for more than a minute.
The atomic mass of iron-56 is 55.93 u. Find the mass of one iron-56 atom in kilograms.
1 u = 1.66 × 10⁻²⁷ kg.
For ²³⁸₉₂U and ¹⁹⁷₇₉Au, find the number of protons, neutrons and nucleons. How many electrons does a neutral gold atom have?
Protons = Z, nucleons = A, neutrons = A − Z.
Chlorine has two isotopes of masses 34.98 u and 36.98 u, with relative abundances 75.4 % and 24.6 %. Find the atomic mass of chlorine.
M̄ = Σ pᵢ mᵢ with the abundances as fractions.
Boron has two isotopes, ¹⁰B (10.01 u) and ¹¹B (11.01 u). Its atomic mass is 10.81 u. Find the abundance of each isotope.
Let the fraction of ¹⁰B be x: 10.01 x + 11.01 (1 − x) = 10.81.
Show that Avogadro's number of atoms, each of mass 1 u, has a total mass of about 1 g. (N_A = 6.022 × 10²³)
Multiply N_A by 1.66 × 10⁻²⁷ kg.
Take 1 u = 1.66 × 10⁻²⁷ kg. Write the formula first, then click.
Score: 0 / 12
| If the question says… | Write this first | The trap |
|---|---|---|
| "atomic mass unit is defined as" | 1/12 of the mass of a ¹²C atom | Choosing "mass of a hydrogen atom" or "of a proton" |
| "number of neutrons in ᴬ_Z X" | N = A − Z | Giving A, or adding Z instead of subtracting |
| "electrons in an ion" | e = Z − (charge) | Forgetting the ion charge: Cl⁻ has 18, not 17 |
| "average atomic mass of an element" | Σ pᵢ mᵢ | Taking the plain mean of the isotope masses |
| "isotopes have the same" | Z (protons), so the same chemistry | Choosing "same mass number" |
| "ratio of nuclear to atomic volume" | (10⁻⁴)³ = 10⁻¹² | Answering 10⁻⁴ (that is the radius ratio) |
| "neutron discovered by" | Chadwick, 1932 (α on beryllium) | Rutherford (nucleus, 1911) or Thomson (electron) |
| "free neutron" | unstable, mean life ≈ 1000 s | Saying the neutron is unstable inside every nucleus |
Lesson 2 sorts nuclides into isotopes, isobars and isotones, and finds the size and density of the nucleus with R = R₀A^(1/3). Lesson 3 uses the masses from this lesson (m_p, m_n, 1 u) to find the mass defect and binding energy.
Values used: 1 u = 1.66 × 10⁻²⁷ kg (1.660539 × 10⁻²⁷ kg), m_p = 1.00727 u, m_n = 1.00866 u, m_e = 0.00055 u, m(¹H atom) = 1.007825 u, e = 1.6 × 10⁻¹⁹ C, N_A = 6.022 × 10²³ mol⁻¹.
Follow the four steps: understand it, remember it, try it, then prove it with past papers.