Lesson 11 of 11 · 12 min
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Must-know facts
16 facts
- 11 u = 1/12 of the mass of a ¹²C atom = 1.660539 × 10⁻²⁷ kg; its energy equivalent is 931.5 MeV.
- 2Chlorine: isotopes 34.98 u (75.4%) and 36.98 u (24.6%), average 35.47 u.
- 3mp = 1.00727 u = 1.67262 × 10⁻²⁷ kg; mn = 1.00866 u = 1.6749 × 10⁻²⁷ kg; me = 0.00055 u.
- 4Chadwick found the neutron in 1932 (Nobel Prize 1935); a free neutron decays with a mean life of about 1000 s.
- 5Z protons, N neutrons, A = Z + N nucleons; ¹⁹⁷₇₉Au has 79 protons and 118 neutrons.
- 6Isotopes: same Z. Isobars: same A (³₁H, ³₂He). Isotones: same N (¹⁹⁸₈₀Hg, ¹⁹⁷₇₉Au).
- 7R = R₀A^(1/3), R₀ = 1.2 fm, so volume ∝ A and nuclear density is the same for all nuclei, about 2.3 × 10¹⁷ kg m⁻³.
- 8E = mc²: 1 g of matter is equivalent to 9 × 10¹³ J.
- 9Mass defect ΔM = [Zmp + (A − Z)mn] − M; binding energy Eb = ΔMc².
- 10¹⁶O: ΔM = 0.13691 u, Eb = 127.5 MeV.
- 11Ebn is nearly constant (about 8 MeV) for 30 < A < 170, peaks at about 8.75 MeV at A = 56 and is 7.6 MeV at A = 238.
- 12Nuclear force: attractive, much stronger than the Coulomb force, short-ranged (a few fm), repulsive below about 0.8 fm, charge-independent.
- 13Becquerel discovered radioactivity in 1896; the decays are α (⁴₂He), β (electrons or positrons) and γ (photons).
- 14Fission of ²³⁵U by a neutron releases about 200 MeV per nucleus; 1 kg of uranium gives about 10¹⁴ J against 10⁷ J from 1 kg of coal.
- 15Two protons face a Coulomb barrier of about 400 keV; the sun's core is at 1.5 × 10⁷ K.
- 16Proton–proton cycle: four hydrogen atoms make one helium atom and release 26.7 MeV.
Common traps
Where marks are lost
Saying heavier nuclei are denser because they hold more nucleons.
Using atomic masses for the mass defect but leaving out the electrons.
Treating the largest total binding energy as the most stable nucleus.
Thinking the nuclear force acts between every pair of nucleons in a nucleus.
Claiming the numbers of protons and neutrons change in fission, releasing mass.
Saying mass–energy conversion never happens in chemical reactions.
Formulas
8 to know
Atomic mass unit
1 u = (mass of ¹²C atom)/12 = 1.660539 × 10⁻²⁷ kg
Energy equivalent 931.5 MeV.
Mass number
A = Z + N
Z protons, N neutrons.
Nuclear radius
R = R₀A^(1/3)
R₀ = 1.2 fm = 1.2 × 10⁻¹⁵ m.
Mass–energy equivalence
E = mc²
c ≈ 3 × 10⁸ m s⁻¹.
Mass defect
ΔM = [Zmp + (A − Z)mn] − M
M is the mass of the nucleus.
Binding energy
Eb = ΔMc²
1 u × c² = 931.5 MeV.
Binding energy per nucleon
Ebn = Eb/A
About 8 MeV for 30 < A < 170.
Q-value
Q = (sum of initial masses − sum of final masses)c²
Positive Q: energy released.
Key terms
13 terms
- Atomic mass unit
- One-twelfth of the mass of a carbon-12 atom, 1.660539 × 10⁻²⁷ kg.
- Isotopes
- Nuclides of one element: same Z, different N and A.
- Isobars
- Nuclides with the same mass number A.
- Isotones
- Nuclides with the same neutron number N but different Z.
- Nucleon
- A proton or a neutron.
- Nuclide
- A nuclear species, written ᴬ_ZX.
- Mass defect
- How much less a nucleus weighs than its separate protons and neutrons.
- Binding energy
- Energy needed to pull a nucleus fully apart into free nucleons, Eb = ΔMc².
- Saturation
- A nucleon interacts only with its close neighbours, so Ebn stays nearly constant.
- Fission
- A heavy nucleus splitting into two intermediate-mass fragments.
- Fusion
- Light nuclei joining into a heavier, more tightly bound nucleus.
- Coulomb barrier
- The electric repulsion two nuclei must overcome to come within reach of the nuclear force.
- Thermonuclear fusion
- Fusion driven by raising the temperature so that nuclei move fast enough to overcome the barrier.