What traumatic event does Zitkala-Sa describe at the school?

The forcible cutting of her long hair

Why was the cutting of her hair so humiliating to Zitkala-Sa?

Among her people, shingled hair was worn by cowards and mourners

How does nuclear radius depend on mass number?

\(R=R_0 A^{1/3}\), so nuclear density is nearly the same for all nuclei.

The difference between the total mass of free nucleons and the actual mass of the nucleus.

How is binding energy related to mass defect?

\(E_b=\Delta m\,c^2\); the released energy equals the mass defect times \(c^2\).

Why is iron the most stable nucleus?

It has the highest binding energy per nucleon (near \(A=56\)), so it is most tightly bound.

State the law of radioactive decay.

\(N=N_0 e^{-\lambda t}\); the number of undecayed nuclei falls exponentially with time.

Relate half-life and decay constant.

\(T_{1/2}=\dfrac{0.693}{\lambda}\), the time for half the sample to decay.

What changes in alpha and beta decay?

Alpha decay reduces \(A\) by 4 and \(Z\) by 2; beta-minus decay raises \(Z\) by 1 with \(A\) unchanged.

What is a chain reaction in fission?

Neutrons released by one fission trigger further fissions, sustaining the process.

Why does fusion require very high temperature?

To overcome the strong electrostatic repulsion between positively charged nuclei.

Nuclear fusion of hydrogen into helium, releasing vast energy.

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

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The nuclear radius depends on mass number A as:

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