Twenty-eight multiple choice questions with an answer key at the end. No question from this chapter appeared in any paper I could extract or recover, so every question here is built to the AAI pattern and to the difficulty the domain section has shown elsewhere.
30questions
35 minsuggested time
0verified PYQs
MCQformat throughout
Score0 correct · 0 of 30 attempted
Before you begin
Formulas you will need
Key formulas
Nuclear radius: R = R₀A1/3, with R₀ ≈ 1.2 fm · nuclear density is the same for every nucleus
Mass defect Δm = (Zmp + Nmn) − M · Binding energy = Δm × 931.5 MeV per u
Radioactive decay: N = N₀e−λt · Half-life T = 0.693 ∕ λ · after n half-lives a fraction (½)n remains
Alpha decay: A − 4, Z − 2 · Beta-minus: A unchanged, Z + 1 · Gamma: both unchanged
How to use this worksheet. Count half-lives rather than dividing times — 90 minutes with a 30 minute half-life is three halvings, giving 1/8, not 1/3. And read whether a question asks for the fraction remaining or the fraction decayed, because the two are always different.
Section A · Level 1
Nuclear structure, mass defect and decay laws
Ten questions. None should take more than twenty seconds.
Q1
The nucleus of an atom contains:
Protons and neutrons together are called nucleons. Electrons orbit outside the nucleus.
Q2
Nuclides having the same atomic number but different mass numbers are called:
Isotopes share the number of protons but differ in neutrons, so they are the same element chemically.
Q3
Nuclides having the same mass number but different atomic numbers are called:
Isobars have the same total number of nucleons but belong to different elements.
Q4
The radius of a nucleus of mass number A is proportional to:
R = R₀A1/3. Since volume goes as R³, this means the volume is proportional to A.
Q5
The density of nuclear matter is:
Mass goes as A and volume also goes as A, so the density cancels out and is roughly constant at about 2.3 × 1017 kg/m³.
Q6
The difference between the sum of the masses of the free nucleons and the actual nuclear mass is called the:
That missing mass, the mass defect, has been converted into the binding energy that holds the nucleus together.
Q7
One atomic mass unit is equivalent to:
Using E = mc², one unified mass unit corresponds to 931.5 MeV of energy.
Q8
In alpha decay, the mass number of the nucleus:
An alpha particle is a helium nucleus, so the parent loses 4 from its mass number and 2 from its atomic number.
Q9
In beta-minus decay, the atomic number:
A neutron converts into a proton and an electron, so Z rises by one while A is unchanged.
Q10
In gamma emission, the mass number and atomic number:
A gamma ray carries away energy but no nucleons and no charge, so the nucleus simply drops to a lower energy state.
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Section B · Level 2
Binding energy, half-life and nuclear radius
Ten questions. Count half-lives rather than dividing the times.
Q11
A nucleus has a mass defect of 0.02 u. Its binding energy is closest to:
Binding energy = 0.02 × 931.5 = 18.63 MeV.
Q12
After three half-lives, the fraction of a radioactive sample remaining is:
Each half-life halves the amount, so three of them leave (½)³ = 1/8.
Q13
A sample has a half-life of 30 minutes. After 90 minutes the fraction remaining is:
90 minutes is three half-lives, so 1/8 remains. Option 2 comes from dividing the times rather than halving repeatedly.
Q14
The relation between half-life T and decay constant λ is:
T = ln2 ∕ λ = 0.693 ∕ λ, so a larger decay constant means a shorter half-life.
Q15
Two nuclei have mass numbers 1 and 27. The ratio of their radii is:
Radius goes as A1/3, and the cube root of 27 is 3, so the ratio is 1 : 3.
Q16
Two nuclei have mass numbers 8 and 64. The ratio of their radii is:
The cube roots are 2 and 4, so the radii are in the ratio 2 : 4, which is 1 : 2.
Q17
The binding energy per nucleon is greatest for nuclei with mass number near:
The curve peaks at about 8.8 MeV per nucleon near iron-56, which is why iron is the most stable nucleus.
Q18
The energy released in the fission of one uranium-235 nucleus is about:
Each fission releases roughly 200 MeV, which is around a million times the energy of a chemical reaction per atom.
Q19
After two half-lives, the fraction of a sample that has decayed is:
One quarter remains, so three quarters has decayed. Reading the question carefully — remaining versus decayed — matters here.
Q20
The activity of a radioactive sample is measured in:
One becquerel is one disintegration per second. The curie is the older, much larger unit.
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Section C · Level 3
Nuclear forces, fission, fusion and reactors
Eight questions. Think in terms of the binding energy per nucleon curve.
Q21
Energy is released in nuclear fission because the binding energy per nucleon of the products is:
Moving towards the peak of the curve means the nucleons become more tightly bound, and the surplus energy is released.
Q22
Energy is released in nuclear fusion because light nuclei combine to form a nucleus with:
Light nuclei sit low on the curve, so fusing them moves them upward towards greater stability and releases energy. Both fission and fusion work by climbing the same curve from opposite ends.
Q23
Nuclear forces are:
The strong nuclear force acts over about a femtometre but is far stronger than electrostatic repulsion at that range, which is what holds a nucleus together.
Q24
Nuclear forces are said to be charge independent because they act:
Proton-proton, neutron-neutron and proton-neutron attractions are essentially the same strength.
Q25
The half-life of a radioactive substance does not depend on:
Radioactive decay is a nuclear process, entirely unaffected by chemical or physical conditions outside the nucleus.
Q26
A radioactive nucleus emits an alpha particle followed by two beta-minus particles. Compared with the original, the final nucleus is:
Alpha decay lowers Z by 2 and the two beta decays raise it by 2, so Z returns to its original value while A has fallen by 4. Same element, different mass number, which is an isotope.
Q27
Why is a chain reaction possible in uranium fission?
Each fission releases on average two or three neutrons, and those can trigger further fissions. Controlling how many go on to do so is exactly what a reactor's control rods manage.
Q28
In a nuclear reactor, the moderator is used to:
Slow neutrons are far more likely to cause fission in uranium-235, so a moderator such as graphite or heavy water reduces their speed. Control rods, by contrast, absorb neutrons.
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Answer key
Answers
Check only after you have attempted every question. Tap any question above to see the full worked solution.
All thirty questions with the formula sheet printed on the front page and ruled working space for your circuit reductions. Print it, solve it, keep it.
Seven questions from one chapter in a single year.
Live classes cover the full Class 11 and 12 physics and maths syllabus for AAI ATC, taught from the real question papers with the method for each question type drilled until it is automatic.