Is Nuclei part of the EAPCET Physics syllabus?

Yes. Nuclei is taught in Intermediate second year Physics, and the EAPCET Engineering syllabus is based on the Intermediate first- and second-year syllabus. Check the official notification each year for any changes.

How many Physics questions are there in EAPCET?

40 of the 160 questions in the Engineering paper are Physics, spread across 30 chapters.

What mistakes do students make in Nuclei?

Confusing the fraction remaining with the fraction decayed — after n half-lives, 1/2ⁿ remains and 1 − 1/2ⁿ has decayed. Treating half-life and mean life as equal — mean life τ = 1/λ is longer, with T½ = 0.693τ. Comparing total binding energies to judge stability — compare binding energy per nucleon instead. Changing the mass number in β-decay — β decay changes Z by one but leaves A unchanged.

EAPCET Physics · Intermediate second year

Nuclei

Nuclei covers nuclear size, mass defect and binding energy, radioactive decay, and fission and fusion.

Subject: Physics
Taught in: Intermediate second year
Physics in the paper: 40 of 160 questions

Key formulas and results

Nuclear radius $R = R_{0}A^{1/3}$ ; nuclear density is the same for all nuclei
Binding energy $= \Delta m\,c^{2}$ , with $1\ \text{u} \approx 931.5\ \text{MeV}$
$N = N_{0}e^{-\lambda t}$
Half-life $T_{1/2} = \frac{0.693}{\lambda}$ ; mean life $\tau = \frac{1}{\lambda}$
Binding energy per nucleon peaks near $A \approx 56$ (iron)
Mass defect: $\Delta m = [Zm_{p} + (A - Z)m_{n}] - M_{\text{nucleus}}$
Binding energy per nucleon $= \text{BE}/A$
Energy released in a nuclear reaction: Q = (total binding energy of products) − (total binding energy of reactants)
Typical fission of uranium-235: $\ce{^{235}U + n -> ^{144}Ba + ^{89}Kr + 3n}$ + energy
Fusion reactions of hydrogen isotopes: $\ce{^{2}H + ^{2}H -> ^{3}H + ^{1}H}$ + energy; $\ce{^{3}H + ^{2}H -> ^{4}He + n}$ + energy

What this chapter covers

Nuclear size and density
Mass defect and binding energy
Radioactivity and decay law
Half-life and mean life
Fission and fusion

How it is usually asked

Half-life calculations
Binding energy
Decay products
Fission and fusion

Understanding Nuclei

A nucleus is made of protons and neutrons held together by the strong nuclear force. Its radius grows as A^(1/3), so its volume is proportional to A, which makes nuclear density the same for all nuclei. The mass of a nucleus is slightly less than the total mass of its separate nucleons; this mass defect, converted using E = mc², is the binding energy.

Binding energy per nucleon is highest near iron. Heavy nuclei can therefore release energy by splitting (fission) and very light nuclei by joining (fusion). Radioactive decay is random for a single nucleus, but a large sample follows N = N₀e^(−λt). The half-life is 0.693/λ and the mean life is 1/λ. Alpha decay lowers A by 4 and Z by 2; β⁻ decay raises Z by 1 and leaves A unchanged.

EAPCET typically tests half-life calculations, binding energy from mass defect, the products of a chain of decays, and comparisons between fission and fusion. For a decay chain, first use the change in mass number to count the alpha decays, since only alpha decay changes A (by 4 each time); then use the change in atomic number to find how many β⁻ decays are needed to balance the charge.

Worked example

EAPCET-style question

A radioactive sample has a half-life of 20 minutes. What fraction of the original nuclei remains undecayed after 1 hour?

(1) $\frac{1}{8}$
(2) $\frac{7}{8}$
(3) $\frac{1}{3}$
(4) $\frac{1}{6}$

Solution

Number of half-lives $n = \frac{60\ \text{min}}{20\ \text{min}} = 3$ .
Fraction remaining $= \frac{1}{2^{n}} = \frac{1}{2^{3}}$ .
Fraction remaining $= \frac{1}{8}$ (the fraction that has decayed is $\frac{7}{8}$ ).

Answer: $\frac{1}{8}$

Shortcuts and results to remember

A higher binding energy per nucleon means a more stable nucleus; energy is released whenever the products are more tightly bound than the reactants.
Heavy nuclei release energy by fission and light nuclei by fusion, because both move towards the peak of the BE/A curve near $A \approx 56$ .
In a reactor the moderator (heavy water or graphite) slows neutrons, control rods (cadmium or boron) absorb extra neutrons, and the coolant removes heat.
In any exothermic nuclear reaction the total mass of the products is less than the total mass of the reactants.

Common mistakes to avoid

Confusing the fraction remaining with the fraction decayed — after n half-lives, 1/2ⁿ remains and 1 − 1/2ⁿ has decayed.
Treating half-life and mean life as equal — mean life τ = 1/λ is longer, with T½ = 0.693τ.
Comparing total binding energies to judge stability — compare binding energy per nucleon instead.
Changing the mass number in β-decay — β decay changes Z by one but leaves A unchanged.

How to prepare it

After n half-lives, N₀/2ⁿ remains — most decay questions are this in disguise.

Once the formulas feel familiar, test them the way the exam does: practise Nuclei questions chapter-wise, then attempt a full previous year paper to see whether it holds up under a 3-hour timer.

Related Physics chapters

See every chapter in the EAPCET Physics syllabus.

Practise Nuclei chapter-wise

Chapter-wise quizzes show exactly which topics in this chapter you still get wrong — before a full paper does.

Frequently asked questions

Is Nuclei part of the EAPCET Physics syllabus?: Yes. Nuclei is taught in Intermediate second year Physics, and the EAPCET Engineering syllabus is based on the Intermediate first- and second-year syllabus. Check the official notification each year for any changes.
How should I prepare Nuclei for EAPCET?: After n half-lives, N₀/2ⁿ remains — most decay questions are this in disguise.
How many Physics questions are there in EAPCET?: 40 of the 160 questions in the Engineering paper are Physics, spread across 30 chapters.
What mistakes do students make in Nuclei?: Confusing the fraction remaining with the fraction decayed — after n half-lives, 1/2ⁿ remains and 1 − 1/2ⁿ has decayed. Treating half-life and mean life as equal — mean life τ = 1/λ is longer, with T½ = 0.693τ. Comparing total binding energies to judge stability — compare binding energy per nucleon instead. Changing the mass number in β-decay — β decay changes Z by one but leaves A unchanged.