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Nuclear Physics revision notes

Every idea in the Nuclear Physics chapter for JEE Main, with the usual mistakes and the fast methods. Topic 1 is open to everyone; sign in free to read all 17 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that concept, and "last" is the latest year one appeared. ★ marks ideas asked 8 or more times.

Composition and size of the nucleus

Composition of the nucleus
4× asked, last 2024
ZAX,N=A−Z,1 u=1.66×10−27 kg≡931.5 MeV/c2{}^{A}_{Z}X,\qquad N=A-Z,\qquad 1\ \text{u}=1.66\times10^{-27}\ \text{kg}\equiv931.5\ \text{MeV}/c^2
Isotopes: same ZZ. Isobars: same AA. Isotones: same NN. Isomers: same AA and ZZ, different energy state.
  • 1 u =1/12=1/12 of the mass of one 12{}^{12}C atom. Average atomic mass of an element =∑fiMi=\sum f_iM_i over its isotopes (fif_i = abundance fraction). Cl: 0.754(34.98)+0.246(36.98)≈35.470.754(34.98)+0.246(36.98)\approx35.47 u.
Nuclear radius
8× asked, last 2025
R=R0A1/3,R0≈1.2 fm=1.2×10−15 mR=R_0A^{1/3},\qquad R_0\approx1.2\ \text{fm}=1.2\times10^{-15}\ \text{m}
Volume ∝R3∝A\propto R^3\propto A; R1/R2=(A1/A2)1/3R_1/R_2=(A_1/A_2)^{1/3}. ln⁡(R/R0)\ln(R/R_0) against ln⁡A\ln A: a line through the origin, slope 1/31/3.
  • Quick method. Ratio of radii given: cube it to get the ratio of mass numbers. Half the radius means one-eighth of AA; radius ×21/3\times2^{1/3} means A×2A\times2.
Nuclear density
9× asked, last 2025
ρ=A mN43πR03A=3mN4πR03≈2.3×1017 kg/m3\rho=\frac{A\,m_N}{\tfrac43\pi R_0^3A}=\frac{3m_N}{4\pi R_0^3}\approx2.3\times10^{17}\ \text{kg/m}^3
mNm_N = mass of one nucleon. Same for every nucleus, about 101410^{14} times the density of water. ρ∝1/R03\rho\propto1/R_0^3.
  • Not a higher density for heavier nuclei. Mass and volume both grow as AA, so ρ\rho does not depend on AA. Any ordering of nuclear densities by mass number is false, though R∝A1/3R\propto A^{1/3} is true.

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14 more concepts in 4 topics

Mass defect and binding energy; Nuclear reactions and Q value; Fission and fusion; and Radioactivity (dropped 2024, still asked). Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Mass defect and binding energy

  • Mass–energy equivalence5×
  • Mass defect and binding energy6×
  • Binding energy per nucleon7×
  • Binding energy curve7×
  • Nuclear force3×

Nuclear reactions and Q value

  • Balancing a nuclear reaction6×
  • Q value of a reaction15×
  • Energy from a sample of fuel5×

Fission and fusion

  • Nuclear fission8×
  • Break-up of a nucleus at rest7×
  • Nuclear fusion6×

Radioactivity (dropped 2024, still asked)

  • Decay law and half-life35×
  • Alpha, beta and gamma decay8×
  • Parallel and successive decay8×

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