Lesson 11 of 11 · 12 min
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Must-know facts
16 facts
- 011 u = 1/12 of the mass of a ¹²C atom = 1.660539 × 10⁻²⁷ kg; its energy equivalent is 931.5 MeV.
- 02Chlorine: isotopes 34.98 u (75.4%) and 36.98 u (24.6%), average 35.47 u.
- 03mp = 1.00727 u = 1.67262 × 10⁻²⁷ kg; mn = 1.00866 u = 1.6749 × 10⁻²⁷ kg; me = 0.00055 u.
- 04Chadwick found the neutron in 1932 (Nobel Prize 1935); a free neutron decays with a mean life of about 1000 s.
- 05Z protons, N neutrons, A = Z + N nucleons; ¹⁹⁷₇₉Au has 79 protons and 118 neutrons.
- 06Isotopes: same Z. Isobars: same A (³₁H, ³₂He). Isotones: same N (¹⁹⁸₈₀Hg, ¹⁹⁷₇₉Au).
- 07R = 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.
- 08E = mc²: 1 g of matter is equivalent to 9 × 10¹³ J.
- 09Mass 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
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.