Chapter 6 — Atomic models, radiation and scientific reasoning
Why an atomic model is a model
A scientific model is a structured explanation that accounts for observations and makes predictions. It is not a tiny photograph of an atom. Early atomic models changed as experiments revealed effects they could not explain. In an MCQ, identify which observation a model addressed rather than treating a scientist's name as an isolated pair to memorise. Thomson's model pictured negative electrons in a spread-out positive background. Geiger and Marsden's scattering measurements, interpreted by Rutherford, pointed to a small, dense, positively charged nucleus and an atomic volume that is mostly empty space in that model. A simple planetary picture captures parts of that insight, but an electron is not literally a miniature planet on a visible fixed track.
Bohr's model introduced allowed energy levels for electrons in a simplified atom, helping explain selected line spectra, especially hydrogen. Modern quantum theory describes electron states more richly than fixed circular orbits. A candidate should know the school-level progression and its limits: new evidence refines or replaces a model; it does not make every earlier observation meaningless. A matching question may combine scientist, experiment and conclusion. Trace the evidence first: rare large-angle alpha scattering supports a concentrated nucleus; a line spectrum supports discrete energy differences in the model.
Count the parts before naming the atom
An atom's atomic number Z is its number of protons. A neutral atom has the same number of electrons as protons. Mass number A is the total number of protons and neutrons, so neutrons = A−Z. Carbon-14 has Z=6 and A=14: it contains 6 protons and 8 neutrons, with 6 electrons when neutral. A carbon-14 ion could have a different electron count without changing its proton and neutron counts. This is why “atom,” “ion” and “isotope” cannot be swapped carelessly in a numerical question.
Isotopes are atoms of the same element with the same Z but different neutron counts and therefore different A values. Isobars have the same mass number but different atomic numbers, so they belong to different elements. For example, an idealised pair with A=40 and Z=18 versus A=40 and Z=20 are isobars; their proton counts differ. The labels encode the answer. When a question gives nuclide notation with A at upper left and Z at lower left, write a short P-N-E table. For neutral atoms, P=Z, N=A−Z, E=Z; for a positive ion, electrons are fewer by the magnitude of the positive charge.
The nucleus contains nearly all atomic mass in the basic school model. Electrons have much smaller mass than protons and neutrons. A proton carries positive elementary charge, an electron an equal-magnitude negative charge, and a neutron is electrically neutral. “Neutral neutron” is not the same as an electrically neutral atom: the latter has balancing positive and negative charges. When an atom becomes a cation by losing electrons, its nucleus does not lose protons in an ordinary chemical ionisation process.
Radiation types and what can be inferred
Radioactivity is a change involving an unstable nucleus. Alpha radiation consists of helium nuclei; beta radiation in the simple beta-minus case consists of high-energy electrons; gamma radiation is electromagnetic radiation. Their charge and mass differ, which affects how they interact with matter. Alpha carries +2 elementary charge and is comparatively massive. A beta-minus particle carries −1 elementary charge. A gamma photon has no electric charge and no rest mass. Be precise about the beta process: other beta-decay modes exist, so the exam stem's beta type matters if detailed nuclear changes are asked.
An alpha emission lowers mass number by four and atomic number by two because the outgoing helium nucleus takes two protons and two neutrons. In beta-minus decay, a neutron converts into a proton while an electron and antineutrino are emitted; mass number stays the same and atomic number rises by one. Gamma emission usually changes the nucleus's energy state without changing A or Z. These bookkeeping rules are a safer route than memorising a table of example nuclides. Write A and Z on both sides of a proposed nuclear equation and check that the relevant totals balance.
Different radiation types have different penetration and ionisation patterns, but a diagram of one barrier is not universal safety guidance. A sheet of paper can stop many alpha particles from an external source, while an alpha-emitting substance can still be hazardous if taken into the body. Gamma radiation can penetrate more deeply and requires context-dependent shielding. This chapter teaches classification for exam questions. It does not offer handling or exposure instructions. Radiation risk depends on source, energy, duration, geometry and whether material is internal or external; a single “safe distance” fact is not justified by a textbook comparison chart.
Half-life is the time for the expected number of undecayed nuclei in a large sample to fall to half its previous value. If an idealised sample begins with 800 countable unstable nuclei and has a half-life of 5 hours, the expected remaining amounts after 5, 10 and 15 hours are 400, 200 and 100. The decay process of a single nucleus is probabilistic; half-life does not mean every nucleus waits exactly five hours and then changes. If a question asks for the fraction after three half-lives, the answer is (1/2)³ = 1/8. Subtracting a fixed 50% of the original amount each time would be wrong after the first interval.
X rays are electromagnetic radiation often generated by an instrument rather than by the radioactive decay of its material. An X-ray machine's radiation production can cease when its beam is switched off, whereas a radioactive source's nuclear decays follow the isotope's half-life. This distinguishes a machine-generated radiation field from the behaviour of a radioactive substance. In a school-level MCQ, do not classify every ionising radiation source as “radioactive.” The same word “radiation” is used broadly, so examine the physical origin described.
Energy from atoms and light
Nuclear fission splits a heavy nucleus into smaller nuclei and can release energy. Nuclear fusion combines light nuclei into heavier ones under suitable conditions and powers the Sun in the standard stellar account. A chemical burning reaction rearranges electrons and bonds; it does not split an atomic nucleus. Thus “the Sun burns coal” is a poor scientific explanation of solar energy. The term “nuclear” names the scale and process, not a claim that every application is identical or has the same hazard.
The photoelectric effect describes electrons being emitted from a material when appropriate light falls on it. In the simple photon model, each photon carries energy related to its frequency. More intensity at too-low a frequency does not necessarily cause emission from a material with a threshold; sufficiently high frequency is essential in the idealised description. This phenomenon helped establish the quantum account of light, associated with Einstein's Nobel-recognised work. A matching question that asks why Einstein received his 1921 Physics Nobel should be read against that contribution, not answered “relativity” by fame alone.
Evidence and measurement before authority
An experimental claim becomes stronger when it specifies the observable, the method and the conditions. If two materials show different detector counts, ask whether the measurement time, distance, background and instrument response were controlled before attributing the difference to the material. The same reasoning applies in non-nuclear science: an observed correlation is not automatically a cause. A conductor's resistance may rise while current rises because the conductor warms; a straight-line V–I law cannot be inferred without checking the relevant conditions.
Use units as an evidence check. Frequency is measured in hertz, wavelength in metres and energy in joules. Half-life is a duration, so seconds, hours or years may be used; it is not measured in becquerels. Activity, which counts decays per unit time, uses the becquerel (Bq). A dose quantity has its own unit and meaning and should not be inferred from activity alone. This book avoids dose calculations because they require specialist context beyond the planned police-exam practice. In an MCQ, the safest first step is to identify the physical quantity before reading the unit options.
Separate observation from inference
In the thin-foil scattering experiment, most alpha particles passed through with little deflection, some were deflected and a very small fraction changed direction substantially. The observation was a pattern of particle deflections. The inference was that positive charge and much of the atom's mass occupy a small region, with most of the atomic volume relatively empty in that model. “Rutherford photographed the nucleus” is therefore a different and incorrect description. An experiment can provide strong evidence for an unseen structure by testing the consequences of competing models. Matching questions are easier when the observation and the explanation are kept in separate columns.
No single early model explained every atomic property. Thomson's picture included electrons but did not explain the concentrated scattering centre. Rutherford's nuclear picture accounted for scattering but did not, by classical orbital reasoning alone, explain stable atomic electron arrangements or discrete spectral lines. Bohr's quantised levels addressed important features of hydrogen's spectrum, while later quantum theory replaced the literal orbit picture with a fuller account of electron states. An earlier model can remain useful for a limited calculation without being a complete physical description. This is why school diagrams often show shells even though modern theory uses orbitals; the diagram is a teaching representation whose scope must be understood.
A particle-counting table for ions and isotopes
Take a nuclide with mass number 23 and atomic number 11. Its nucleus contains 11 protons and 12 neutrons. The neutral atom contains 11 electrons; a singly positive ion contains 10 electrons. The positive charge follows from 11 positive proton charges and only 10 negative electron charges. Removing an electron does not change the mass number from 23 to 22, because mass number counts nucleons rather than all particles. Although the atom's actual mass changes slightly when an electron is lost, the integer mass number remains unchanged. This distinction prevents an overly literal use of the phrase “mass number.”
Now compare a nuclide with A=24 and Z=11. It has one extra neutron and is an isotope of the first because proton count is unchanged. A nuclide with A=23 and Z=12 instead has a different proton count and belongs to another element; the equal mass numbers make the pair isobars. To identify isotones, compare neutron counts: a nuclide with A=24 and Z=12 has 12 neutrons, matching the first example's neutron count even though the elements differ. These three labels test three different equalities: same Z for isotopes, same A for isobars and same A−Z for isotones. Calculate before naming the relationship.
Mass number is also different from relative atomic mass. A mass number belongs to a particular isotope and is an integer nucleon count. A quoted relative atomic mass for an element can reflect an abundance-weighted average of its naturally occurring isotopes. In a synthetic example, suppose 75% of atoms have isotopic mass approximated as 20 units and 25% as 22 units. The weighted mean mass is 0.75×20+0.25×22=20.5 u. Relative atomic mass is the ratio of that mean mass to the atomic mass constant, so its corresponding value is 20.5 with no unit. No individual nucleus needs a mass number of 20.5. The fractional average reflects a mixture. Real calculations use isotopic masses, not simply rounded mass numbers, but the simple arithmetic shows why an element's listed average need not be an integer.
Half-life calculations with an independent check
The fraction remaining after n half-lives is 1/2ⁿ. If a sample falls to 25% of its initial radioactive parent population, two half-lives have elapsed because 100%→50%→25%. If that change takes 18 hours, the half-life is 18/2=9 hours. If only 6.25% remains, four half-lives have elapsed: 100%→50%→25%→12.5%→6.25%. These reverse questions ask for the number of halvings first. Dividing total elapsed time by the percentage remaining has no physical meaning and gives the wrong units as well as the wrong result.
Distinguish the fraction remaining from the fraction decayed. After three half-lives, 1/8 remains and 7/8 has decayed. For an initial 800 units, the remaining parent population is 100 units and 700 units have changed. “Seven eighths decayed” does not mean seven eighths of the total sample necessarily disappeared: the daughter products can remain in the material. A question about remaining parent nuclei is therefore different from a question about the total mass of everything in a closed container. Use the quantity explicitly named in the stem.
Activity is proportional to the number of undecayed parent nuclei for a single isotope with a fixed decay constant. Its activity therefore halves along with that population. Measured detector counts, however, can include a background contribution. Suppose a detector records 220 counts per minute initially and the separately measured background is 20 counts per minute. The initial net count rate attributable to the source is 200. After one half-life, under the same counting conditions, the net rate would be 100 and the total expected reading 120, rather than 110. Subtract background before applying the half-life factor, then add it back if the question asks for the detector's total reading. This is a synthetic data exercise, not an exposure assessment.
Read a statement about radiation precisely
Alpha and beta particles can be deflected by electric or magnetic fields because they carry charge; gamma photons have no electric charge and do not follow the same charged-particle deflection rule. The degree and direction of deflection depend on particle charge, speed and other conditions, so a simple ranking requires the assumptions in the question. A positively charged alpha particle and a negatively charged beta-minus particle respond in opposite directions to a specified electric field. Gamma radiation's lack of charge does not make it incapable of interacting with matter; it can transfer energy through other processes. Charge, penetration and biological effect are separate properties.
The word “beta” needs care. Beta-minus emission increases Z by one without changing A; beta-plus emission decreases Z by one without changing A. In either case, the electron or positron is produced in the nuclear transformation, rather than being an ordinary orbital electron shaken out of the atom. Gamma emission changes nuclear energy without the A and Z change characteristic of alpha or beta decay. A question that simply asks whether beta is positively or negatively charged may be using the traditional beta-minus classroom case; a precise question should name the mode when the distinction affects the answer.
Retrieval exercise with explained answers
Try four short checks before proceeding. First, a neutral atom has A=35 and Z=17: what are its proton, neutron and electron counts? They are 17, 18 and 17. Second, what changes when it forms a singly negative ion? Electron count becomes 18; the nucleus remains the same. Third, what fraction of a parent isotope remains after four half-lives? One sixteenth, or 6.25%. Fourth, does a low detector count by itself establish a low dose to a person? No: source type, energy, geometry, detector response and exposure conditions matter. The first three questions use exact model arithmetic; the fourth tests whether the evidence supports the proposed conclusion.
Worked counting route
A synthetic neutral isotope has atomic number 15 and mass number 31. It contains 15 protons, 31−15=16 neutrons and 15 electrons. If it loses three electrons to form a 3+ ion, the ion has 12 electrons while protons and neutrons remain 15 and 16. If a question instead says an isotope of the same element has mass number 32, only the neutron count changes: it becomes 17. The element remains defined by its 15 protons. This small table distinguishes an isotope change from ordinary ion formation more reliably than a word-only definition.
For a separate synthetic half-life item, suppose 640 units of a radioactive sample remain at the start and half-life is 4 days. After 12 days, three half-lives have passed: 640→320→160→80. The remaining fraction is 80/640=1/8, or 12.5%. No claim is made about a real isotope or actual handling. If an option offers 320−160−80=80 by a confused subtraction, the matching final number may be accidental; the explanation must show repeated halving of the current amount.
Recall and review
Before attempting the chapter's 36 items, state what determines an element's identity, what changes in an isotope, and what changes in an ion. Explain why Rutherford's scattering result challenged a diffuse-positive-charge model. Calculate the particles in carbon-14 and in a simple positive ion. Distinguish alpha, beta-minus and gamma by physical nature and their basic A/Z changes. Halve a synthetic quantity three times and name the fraction remaining. Finally, explain why a model may be useful even when later evidence shows that its literal picture is incomplete. These prompts prepare you for both direct recall and two-statement reasoning items.
Figure 6. Original chapter diagram.
Practice 36 questions
Choose one answer for each item. The answer key and explanations follow this chapter set.
1. An alpha particle is identical to the nucleus of which atom?
A. Hydrogen B. Helium C. Lithium D. Beryllium
2. The energy of the Sun is produced by:
A. Nuclear fusion of hydrogen into helium B. Nuclear fission of uranium C. Burning of coal D. Chemical combustion of hydrogen
3. Radioactivity was discovered in 1896, while working with uranium salts, by which scientist?
A. Marie Curie B. Ernest Rutherford C. Wilhelm Röntgen D. Henri Becquerel
4. Whose 1911 interpretation of alpha-particle scattering by thin gold foil established the nuclear model of the atom?
A. Ernest Rutherford B. J.J. Thomson C. Niels Bohr D. James Chadwick
5. What is the SI unit of density?
A. Gram per cubic centimetre (g/cm³) B. Kilogram per cubic metre (kg/m³) C. Newton per square metre (N/m²) D. Kilogram per square metre (kg/m²)
6. Which of the following has the same value everywhere in the universe?
A. Acceleration due to gravity (g) B. Weight of a body C. Escape velocity D. Universal gravitational constant (G)
7. Arrange the following discoveries in the order in which they were made.
A. Discovery of the electron
B. Discovery of the proton
C. Discovery of the neutron
D. Discovery of X-rays
A. A, D, B, C B. D, A, C, B C. A, B, D, C D. D, A, B, C
8. In the usual school-level comparison of alpha, beta and gamma radiation, arrange them in increasing typical penetrating power: 1. Gamma rays; 2. Alpha particles; 3. Beta particles.
A. 1, 3, 2 B. 3, 2, 1 C. 2, 1, 3 D. 2, 3, 1
9. Thomson's "plum pudding" model of the atom was disproved by which experiment?
A. Millikan's oil drop experiment B. Thomson's cathode ray experiment C. Chadwick's beryllium radiation experiment D. Rutherford's alpha-particle scattering (gold foil) experiment
10. Match the scientist in List-I with the Nobel Prize in List-II.
List-I: A. Wilhelm Röntgen B. Ernest Rutherford C. James Chadwick D. Otto Hahn
List-II: 1. Chemistry, 1944 2. Physics, 1901 3. Chemistry, 1908 4. Physics, 1935
A. A-2, B-4, C-3, D-1 B. A-2, B-3, C-4, D-1 C. A-3, B-2, C-4, D-1 D. A-2, B-3, C-1, D-4
11. In beta-minus decay of a nucleus, what happens to its mass number A and atomic number Z?
A. A decreases by 1; Z is unchanged B. A is unchanged; Z decreases by 1 C. A is unchanged; Z increases by 1 D. A increases by 1; Z increases by 1
12. The half-life of Carbon-14, used in radiocarbon dating, is approximately:
A. 1,600 years B. 50,000 years C. 4.5 billion years D. 5,730 years
13. How many neutrons are present in the nucleus of a Carbon-14 atom? (Atomic number of carbon = 6)
A. 6 B. 14 C. 8 D. 20
14. In an idealised calculation, how much of a 16 g sample of pure carbon-14 remains undecayed after 17,190 years? Use a half-life of 5,730 years.
A. 4 g B. 8 g C. 2 g D. 1 g
15. Which researchers identified barium among the products of neutron-bombarded uranium in 1938, evidence that led to the discovery of nuclear fission?
A. Enrico Fermi and Leo Szilard B. Otto Hahn and Fritz Strassmann C. Pierre and Marie Curie D. Ernest Rutherford and Frederick Soddy
16. The discovery of the proton (around 1919) is credited to:
A. James Chadwick B. Ernest Rutherford C. J.J. Thomson D. Niels Bohr
17. The radiocarbon (Carbon-14) dating technique was developed by:
A. Willard Libby B. Otto Hahn C. Enrico Fermi D. Ernest Lawrence
18. Which scientist proposed that electrons revolve only in certain fixed orbits (energy levels) without losing energy, and emit or absorb energy only when they jump between them?
A. Ernest Rutherford B. J.J. Thomson C. Niels Bohr D. John Dalton
19. Who discovered the neutron in 1932?
A. James Chadwick B. Ernest Rutherford C. J.J. Thomson D. Niels Bohr
20. Marie Curie named one of the radioactive elements she discovered after her homeland. Which element is it?
A. Radium B. Francium C. Curium D. Polonium
21. Which radioactive isotope has been used as a gamma-ray source in external-beam cancer radiotherapy?
A. Cobalt-60 B. Carbon-14 C. Uranium-238 D. Hydrogen-2 (deuterium)
22. Carbon-12 and Carbon-14 have the same atomic number but different mass numbers. Such atoms are called:
A. Isobars B. Isotopes C. Isotones D. Allotropes
23. In Rutherford's gold foil experiment most alpha particles passed straight through the foil. This showed that:
A. An atom is mostly empty space B. An atom is a solid sphere of positive charge C. Electrons are embedded in positively charged matter D. Alpha particles carry no charge
24. For hydrogen-like atoms, which feature of Bohr’s model explains discrete spectral lines?
A. Electrons are embedded in a positively charged sphere B. Electrons move only in fixed energy levels and emit light when they jump between them C. The nucleus contains neutrons D. Electrons spiral continuously into the nucleus
25. Consider the following statements:
Statement I: The mass of an electron is about 1/1836 of the mass of a proton.
Statement II: A neutron is slightly heavier than a proton.
Which of the above statements is/are correct?
A. Only I B. Only II C. Both I and II D. Neither I nor II
26. Consider the statements. I: X-rays were discovered by Henri Becquerel in 1896. II: X-rays are, by definition, photons emitted by the nucleus in radioactive decay. Which statement(s) is/are correct?
A. Only I B. Only II C. Both I and II D. Neither I nor II
27. In the usual school-level comparison of alpha, beta and gamma radiation, which statement is NOT a property of gamma rays?
A. They are electromagnetic radiation B. They carry a charge of −1 C. They have no rest mass D. They are the most penetrating of alpha, beta and gamma radiation
28. In the usual school-level comparison of alpha and beta radiation, which statement about an alpha particle is NOT correct?
A. It is more penetrating than a beta particle B. It is identical to a helium nucleus C. It carries a charge of +2 D. It can be stopped by a sheet of paper
29. Match the instrument in List I with the quantity it measures in List II.
List I: A. Anemometer; B. Hydrometer; C. Tachometer; D. Sonometer
List II: 1. Rotational speed of an engine (RPM); 2. Frequency of a vibrating string; 3. Wind speed; 4. Density (specific gravity) of liquids
A. A-4, B-3, C-1, D-2 B. A-3, B-4, C-1, D-2 C. A-3, B-4, C-2, D-1 D. A-1, B-4, C-3, D-2
30. Match the instrument in List-I with what it measures in List-II.
List-I: A. Odometer B. Sextant C. Galvanometer D. Manometer
List-II: 1. Small electric currents 2. Angular distance between two objects, used in navigation 3. Distance travelled by a vehicle 4. Pressure of a gas in a closed system
A. A-2, B-3, C-1, D-4 B. A-3, B-2, C-4, D-1 C. A-3, B-2, C-1, D-4 D. A-1, B-2, C-3, D-4
31. Match the physical constant in List-I with its approximate value in List-II.
List-I: A. Speed of light in vacuum B. Planck's constant C. Elementary charge D. Universal gas constant
List-II: 1. 6.626 × 10⁻³⁴ J·s 2. 3 × 10⁸ m/s 3. 8.314 J/(mol·K) 4. 1.602 × 10⁻¹⁹ C
A. A-2, B-1, C-3, D-4 B. A-1, B-2, C-4, D-3 C. A-2, B-1, C-4, D-3 D. A-4, B-1, C-2, D-3
32. How many micrometres (μm) make one millimetre (mm)?
A. 1,000 B. 10 C. 100 D. 10,00,000
33. One standard atmosphere of pressure is approximately:
A. 1.013 × 10³ Pa B. 1.013 × 10⁷ Pa C. 7.6 × 10² Pa D. 1.013 × 10⁵ Pa
34. Using Planck's constant h = 6.626 × 10⁻³⁴ J·s, the energy of a photon of frequency 5 × 10¹⁴ Hz is approximately:
A. 3.3 × 10⁻²⁰ J B. 3.3 × 10⁻¹⁹ J C. 1.3 × 10⁻⁴⁸ J D. 3.3 × 10⁻⁴⁸ J
35. A sound wave of frequency 170 Hz travels in air at 340 m/s. What is its wavelength?
A. 0.5 m B. 1 m C. 4 m D. 2 m
36. The SI unit of inductance, the henry, is named after:
A. Michael Faraday B. Wilhelm Weber C. Joseph Henry D. Heinrich Lenz
Answers and explanations
1. B. An alpha particle consists of 2 protons and 2 neutrons, which is exactly a helium nucleus (charge +2). A hydrogen nucleus is just a single proton, so it is not identical.
2. A. In the Sun's core hydrogen nuclei fuse into helium under extreme heat and pressure, releasing enormous energy by nuclear fusion. Fission (splitting of heavy nuclei) powers today's nuclear reactors, and the Sun does not burn by ordinary chemical combustion.
3. D. Henri Becquerel found in 1896 that uranium salts fogged a photographic plate wrapped in black paper, revealing radioactivity. The Curies later isolated polonium and radium, while Röntgen had discovered X-rays in 1895.
4. A. Ernest Rutherford interpreted the scattering measurements of Hans Geiger and Ernest Marsden and proposed a small, concentrated positive atomic nucleus in 1911. Thomson had proposed the earlier spread-out positive-charge model; Bohr later developed quantised energy levels; Chadwick discovered the neutron.
5. B. Density is mass divided by volume, so its SI unit is kilogram per cubic metre (kg/m³). g/cm³ is a common non-SI unit, N/m² is the pascal (the unit of pressure) and kg/m² is mass per unit area.
6. D. G, the universal gravitational constant (6.674 × 10⁻¹¹ N m²/kg²), is a fixed number everywhere, whereas g, weight and escape velocity depend on the planet and location. Capital G and small g are often confused.
7. D. X-rays were discovered by Röntgen in 1895, the electron by J.J. Thomson in 1897, the proton by Rutherford in 1919 and the neutron by Chadwick in 1932. Hence the order is D, A, B, C.
8. D. The standard qualitative order is alpha < beta < gamma, so 2, 3, 1. Alpha radiation is commonly blocked by paper or skin, beta radiation needs denser shielding, and gamma intensity is reduced by thick shielding. Actual penetration depends on particle energy and material; gamma attenuation is gradual rather than an absolute stopping thickness.
9. D. In the gold foil experiment a few alpha particles bounced back, showing a tiny dense positive nucleus, which the evenly spread charge of the plum pudding model could not explain. Millikan measured the electron's charge; the cathode ray work found the electron.
10. B. Röntgen received the first Nobel Prize in Physics in 1901; Rutherford won the Chemistry prize in 1908 for his work on radioactivity; Chadwick got the Physics prize in 1935 for the neutron; and Hahn the Chemistry prize in 1944 for nuclear fission. Hence A-2, B-3, C-4, D-1.
11. C. In beta-minus decay a neutron changes into a proton while an electron and an antineutrino are emitted. The total number of nucleons A remains the same; the proton count, and hence Z, rises by one. For example carbon-14 (Z = 6) becomes nitrogen-14 (Z = 7).
12. D. The half-life of carbon-14 is about 5,730 years: after that time, half of an initial quantity remains undecayed. The method’s usable dating range depends on contamination, sample preparation and measurement sensitivity; it must not be confused with the half-life. Radium-226 is near 1,600 years, and uranium-238 is near 4.5 billion years.
13. C. Neutrons = mass number − atomic number = 14 − 6 = 8. Carbon-12 has 6 neutrons, so Carbon-14 carries two extra neutrons. 14 is the mass number (protons + neutrons), not the neutron count.
14. C. 17,190 ÷ 5,730 = 3 half-lives. Each half-life halves the remaining amount: 16 → 8 → 4 → 2 g. So 2 g remains undecayed.
15. B. Otto Hahn and Fritz Strassmann identified barium among the products of neutron-bombarded uranium in 1938. Lise Meitner and Otto Frisch then explained the result as nuclear fission in 1939. Fermi and Szilard are associated with early chain-reaction work, rather than this chemical identification.
16. B. Rutherford identified the proton around 1917-1919 by knocking hydrogen nuclei out of nitrogen with alpha particles. Chadwick found the neutron, Thomson the electron, and Bohr gave the shell model.
17. A. Willard Libby developed radiocarbon dating in the late 1940s and received the 1960 Nobel Prize in Chemistry for it. Hahn discovered nuclear fission, Fermi built the first nuclear reactor, and Lawrence invented the cyclotron.
18. C. Niels Bohr (1913) introduced fixed energy levels, fixing the collapse problem of Rutherford's nuclear model and explaining line spectra. Rutherford gave the nucleus, Thomson the plum pudding model and Dalton the indivisible atom.
19. A. James Chadwick, a student of Rutherford, discovered the neutron in 1932 and won the 1935 Nobel Prize in Physics. Thomson discovered the electron (1897), Rutherford the nucleus and proton, and Bohr proposed energy levels.
20. D. Polonium is named after Poland, Marie Curie's homeland; she and Pierre Curie discovered it along with radium in pitchblende. Francium is named after France (discovered later by Marguerite Perey) and curium honours the Curies.
21. A. Cobalt-60 emits gamma photons and has been used in teletherapy equipment for external-beam radiotherapy. Current equipment choices differ by setting. Carbon-14 is associated with dating, uranium-238 belongs to the uranium decay series, and deuterium is a stable hydrogen isotope.
22. B. Isotopes share the atomic number (same element) but differ in neutron count and hence mass number. Isobars have the same mass number but different atomic numbers; isotones share neutron number; allotropes are different structural forms of an element.
23. A. Most alpha particles went straight through, a few were deflected at small angles and a tiny number bounced almost straight back. Rutherford concluded that an atom is mostly empty space with a tiny, dense, positive nucleus; a solid pudding-like atom, as in Thomson's model, could not explain this.
24. B. Bohr’s model assigns permitted electron energies to a hydrogen-like atom. A transition between two levels emits or absorbs a photon whose energy equals their difference, producing a discrete spectral line. The simple Bohr model does not give a complete account of complex many-electron atoms.
25. C. Both are correct. A proton is about 1836 times heavier than an electron, and the neutron's mass (about 1.6749 × 10⁻²⁷ kg) is slightly more than the proton's (about 1.6726 × 10⁻²⁷ kg).
26. D. Neither statement is correct. Wilhelm Röntgen discovered X-rays in 1895; Becquerel found radioactivity in 1896. Gamma rays commonly refer to photons from nuclear transitions, while X-rays generally arise from electronic transitions or rapid deceleration of charged particles. Radioactive decay can induce characteristic X-rays in surrounding atomic electrons, so the origin distinction must be phrased carefully.
27. B. Gamma rays are electrically neutral electromagnetic photons with zero rest mass; charge −1 describes a beta-minus electron. Gamma radiation is generally more penetrating than typical alpha and beta radiation in the standard school comparison, although penetration depends on energy and shielding material and its intensity is attenuated gradually.
28. A. An alpha particle is a helium-4 nucleus with two protons and two neutrons, giving charge +2e. It is ordinarily much less penetrating than beta radiation and may be blocked by paper. Penetration in any real material depends on energy, thickness and composition.
29. B. Anemometer: wind speed (3). Hydrometer: density or specific gravity of liquids (4). Tachometer: engine RPM (1). Sonometer: frequency of a vibrating string (2). Code: A-3, B-4, C-1, D-2.
30. C. An odometer records the distance travelled by a vehicle, a sextant measures the angular distance between two objects for navigation, a galvanometer detects small electric currents and a manometer measures gas pressure in a closed system. Hence A-3, B-2, C-1, D-4.
31. C. The speed of light in vacuum is about 3 × 10⁸ m/s, Planck's constant 6.626 × 10⁻³⁴ J·s, the elementary charge (magnitude of the charge on an electron) 1.602 × 10⁻¹⁹ C and the universal gas constant 8.314 J/(mol·K). Hence A-2, B-1, C-4, D-3.
32. A. Milli = 10⁻³ and micro = 10⁻⁶, so 1 mm = 10⁻³ m = 1,000 × 10⁻⁶ m = 1,000 μm. The figure 10,00,000 is the number of micrometres in one metre, not in one millimetre.
33. D. One standard atmosphere is defined as exactly 101,325 Pa, approximately 1.013 × 10⁵ Pa; it also corresponds to 760 mmHg under the conventional definition. Actual pressure at a sea-level location changes with the weather, so “standard atmosphere” is the precise quantity here.
34. B. Planck's relation gives the photon energy as E = hf = 6.626 × 10⁻³⁴ × 5 × 10¹⁴ = 3.313 × 10⁻¹⁹ J, i.e. about 3.3 × 10⁻¹⁹ J. Dividing h by f (1.3 × 10⁻⁴⁸) is a common slip.
35. D. From the wave equation v = f × λ, λ = v ÷ f = 340 ÷ 170 = 2 m. Dividing the other way (170 ÷ 340) gives the trap 0.5 m. For a fixed speed, frequency and wavelength are inversely related.
36. C. The henry honours the American scientist Joseph Henry, who discovered electromagnetic induction independently of Faraday. Faraday is honoured by the farad (capacitance) and Weber by the weber (magnetic flux).