5 high-yield, syllabus-aligned questions on Modern physics, covering 15 individually creditable mark points. Each one shows the answer that scores full marks under our guide, which phrase earns which mark, and a common incomplete answer — so you can see the difference rather than guess at it.
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Every question and solution is reviewed by examiners versed in WAEC and JAMB, each with more than thirty years of experience.
Mark allocations are TopMarks’ own, written against the published syllabus and Chief Examiners’ reports. They are a guide to how these answers are usually credited, not an official marking scheme.
Define3 marks
Define radioactivity and name the three types of radiation emitted by radioactive substances.
TopMarks model answer
Radioactivity is the spontaneous disintegration of the unstable nucleus of an atom, with the emission of radiation and energy. The three types of radiation emitted are alpha particles, beta particles and gamma rays.
Suggested marking guide
1Spontaneous disintegration of an unstable nucleus
2With emission of radiation or energy
3The three radiations named
Why it scores
Two words carry the first mark. SPONTANEOUS, because radioactive decay is not caused by anything external and cannot be switched on or off. And NUCLEUS, because it is a nuclear process — nothing to do with the electrons, which is why chemical reactions cannot affect it.
A common incomplete answer
“Radioactivity is when a substance gives off alpha, beta and gamma rays.”
What it costs: One mark of three. The three radiations are credited, but the process is never described as the spontaneous disintegration of an unstable nucleus, which is the definition itself.
State three differences between alpha particles and gamma rays.
TopMarks model answer
An alpha particle is a helium nucleus carrying a positive charge, whereas a gamma ray is an electromagnetic wave and carries no charge. Alpha particles have a very short range in air and are stopped by a sheet of paper, while gamma rays are highly penetrating and need thick lead or concrete to absorb them. Alpha particles are strongly ionising while gamma rays are only weakly ionising, and alpha particles are deflected by electric and magnetic fields whereas gamma rays are not.
Suggested marking guide
1Charged particle versus uncharged electromagnetic wave
2Penetrating power
3Ionising power
Why it scores
Ionising power and penetrating power are INVERSELY related, and understanding that gives you the whole comparison from one idea. Alpha particles are strongly ionising precisely BECAUSE they interact so heavily with matter — which is also why they lose energy quickly and cannot penetrate far.
A common incomplete answer
“Alpha particles are stopped by a sheet of paper but gamma rays need thick lead.”
What it costs: Two marks of three. The penetrating power is a properly paired difference and is credited, but charge and ionising power are not mentioned.
State Einstein's photoelectric equation, explaining each term, and define threshold frequency.
TopMarks model answer
Einstein's photoelectric equation is hf = W₀ + Emax, where hf is the energy of the incident photon, W₀ is the work function of the metal and Emax is the maximum kinetic energy of the emitted electron. The threshold frequency is the minimum frequency of incident radiation below which no electron is emitted from the metal surface, however intense the radiation may be.
Suggested marking guide
1The equation with the work function identified
2The maximum kinetic energy of the emitted electron
3Threshold frequency defined
Why it scores
The phrase “however intense the radiation” is the whole point of the threshold frequency, and it is what the photon model explains and the wave model cannot. A very bright red light delivers a great deal of energy and still ejects no electrons, because each individual photon is too weak. Include that clause.
A common incomplete answer
“hf = W₀ + kinetic energy of the electron.”
What it costs: Two marks of three. The equation and the work function are credited, but the kinetic energy is not identified as the MAXIMUM kinetic energy, and threshold frequency is never defined.
Key ideas to include: photon, work function, threshold frequency, maximum kinetic energy, photoelectric emission.
Explain3 marks
Explain what is meant by nuclear fission and nuclear fusion, and state one difference between them.
TopMarks model answer
Nuclear fission is the splitting of a heavy nucleus, such as that of uranium-235, into two lighter nuclei of comparable mass, with the release of neutrons and a large amount of energy. Nuclear fusion is the joining together of two light nuclei, such as those of the isotopes of hydrogen, to form a heavier nucleus, with the release of energy. Fusion releases far more energy per unit mass than fission, but it requires extremely high temperatures to overcome the electrostatic repulsion between the nuclei.
Suggested marking guide
1Fission is the splitting of a heavy nucleus
2Fusion is the joining of light nuclei
3A valid difference between them
Why it scores
Each definition needs the process AND the kind of nucleus it happens to. “Splitting” alone does not distinguish fission from any other break-up; it is the splitting of a HEAVY nucleus into two of comparable size, which is what makes it release energy. The same applies to fusion and light nuclei.
A common incomplete answer
“Fission is the splitting of a heavy nucleus and fusion is the joining of light nuclei.”
What it costs: One mark of three. Both definitions are properly paired and credited, but the question also asked for a difference between the two, and none was given.
Key ideas to include: fission, fusion, heavy nucleus, light nuclei, binding energy, electrostatic repulsion.
Calculate3 marks
A radioactive source has a half-life of 8 days. Calculate the fraction of the original sample remaining after 24 days, and state one use of a radioactive isotope in industry.
TopMarks model answer
Number of half-lives = 24 ÷ 8 = 3. After each half-life the sample is halved, so the fraction remaining is 1/2 x 1/2 x 1/2 = 1/8. In industry a radioactive isotope is used as a thickness gauge: the radiation passing through a sheet of metal or paper is monitored, and any change in the reading indicates a change in the thickness.
Suggested marking guide
1Correct number of half-lives
2Correct fraction remaining
3A valid industrial use
The working, line by line
1Number of half-lives = total time ÷ half-life = 24 ÷ 8 = 3 — Always do this first. It converts the problem into simple halving.
2Fraction remaining = 1/2 x 1/2 x 1/2 = 1/8 — Three half-lives means halving three times, not dividing by three. Write the halvings out.
3One industrial use: thickness gauge — The question has two parts. The use is a whole mark and takes one line.
Why it scores
Radioactive decay is exponential, not linear. Three half-lives leave one eighth, not one third — and the difference between those two answers is entirely a matter of whether the candidate wrote out the halving sequence or did it in their head.
A common incomplete answer
“After 24 days one third of the sample will be left.”
What it costs: All three marks. The number of half-lives is not worked out, the decay is treated as linear when it is exponential, and no industrial use is given.
Key ideas to include: half-life, number of half-lives, exponential decay, thickness gauge, tracer.
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