Nuclei
Class 12 Physics · Physics Part II · Chapter 5
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Summary
The nucleus, made of protons and neutrons (nucleons), has a radius \(R=R_0 A^{1/3}\), giving nearly constant nuclear density independent of mass number. Atomic masses are measured in unified mass units, and the mass of a nucleus is always less than the sum of its constituent nucleons—this mass defect \(\Delta m\) corresponds, through Einstein's \(E=\Delta m\,c^2\), to the binding energy holding the nucleus together. The binding energy per nucleon peaks near mass number 56 (iron), explaining why heavy nuclei release energy on fission and light nuclei on fusion. Radioactivity is the spontaneous decay of unstable nuclei by alpha, beta or gamma emission, governed by the law \(N=N_0 e^{-\lambda t}\), with half-life \(T_{1/2}=\dfrac{0.693}{\lambda}\) and activity proportional to the number of nuclei present. In nuclear fission a heavy nucleus splits, releasing energy and neutrons that can sustain a chain reaction, the basis of reactors and weapons. In fusion, light nuclei combine to form a heavier one with enormous energy release—the process powering the Sun and stars—demonstrating the immense energy locked within the nucleus.
Nuclear size and densityMass defect and binding energyBinding energy curveRadioactivity and decay lawHalf-life and activityFission and fusion
Key terms
Mass defect
Difference between the mass of nucleons and the nuclear mass, \(\Delta m\).
Binding energy
Energy equivalent of the mass defect, \(E_b=\Delta m\,c^2\), holding the nucleus together.
Radioactivity
Spontaneous emission of \(\alpha\), \(\beta\) or \(\gamma\) radiation by unstable nuclei.
Half-life
Time for half the nuclei to decay, \(T_{1/2}=0.693/\lambda\).
Nuclear fission
Splitting of a heavy nucleus into lighter ones with energy release.
Nuclear fusion
Combining of light nuclei into a heavier one with large energy release.
Extra questions & answers
Try one from this chapter
The nuclear radius depends on mass number A as: