3 questions, one for each idea where we can. Answer them, then see which ideas to fix.
Question 1 of 3
Which description of an alpha particle is correct?
Answer and reasoning
AA whole helium atom, electrons included, so it is electrically neutral A student who takes an alpha particle to be a helium atom picks this. The symbol He²⁺ shows that both electrons are missing, so the particle is a nucleus with charge +2e.
BFour nucleons, each carrying charge +e, for a total charge of +4e A student who thinks every nucleon is charged picks this. Two of the four nucleons are neutrons, which are uncharged, so the total charge is +2e.
CA helium-4 nucleus, made of two protons and two neutrons, charge +2eCorrect An alpha particle is a helium-4 nucleus, He²⁺: two protons and two neutrons with no electrons. Only the protons are charged, so its charge is +2e.
DA burst of electromagnetic radiation, with no mass and no charge A student who thinks every emission from a decaying nucleus is an electromagnetic ray picks this. Only gamma rays are electromagnetic radiation; an alpha particle is a helium-4 nucleus with mass and charge +2e.
Working α = ⁴₂He²⁺: 2 protons (charge 2 × (+e) = +2e) + 2 neutrons (charge 0), no electrons; nucleon number 4.
Compared with the nucleus before a beta-minus decay, how many protons and neutrons does the nucleus have after the decay?
Answer and reasoning
AOne fewer proton and one extra neutron A student who thinks the minus sign means the proton number goes down picks this. That is the change in β⁺ decay; in β⁻ decay the emitted charge is −e, so the nucleus gains +e: one more proton.
BNo change: the same protons and neutrons A student who thinks the beta particle is an orbiting electron thrown out of the atom picks this. The electron comes from the nucleus, where a neutron changes into a proton.
COne more proton and one fewer neutronCorrect In β⁻ decay a neutron in the nucleus changes into a proton, emitting an electron and an antineutrino. The nucleus gains a proton and loses a neutron; its nucleon number is unchanged.
DSame number of protons, one fewer neutron A student who thinks the changed neutron is simply lost picks this. The neutron is not lost but becomes a proton, so the proton number rises by 1 and the nucleon number is unchanged.
Carbon-14 nuclei decay by beta-minus emission. A student claims that carbon-11 nuclei must therefore also decay by beta-minus emission. Which is the best evaluation of the claim?
Answer and reasoning
AIt is justified, since all isotopes of an element decay in the same way. A student who thinks the decay type belongs to the element picks this. Different isotopes of one element can decay in different ways, because the type of decay depends on the numbers of protons and neutrons.
BIt is justified if the two samples are kept at the same temperature. A student who thinks conditions such as temperature control how nuclei decay picks this. Temperature affects atoms and electrons, not the nucleus; the type of decay is set by the isotope.
CIt is not justified, since isotopes of an element can decay in different ways.Correct The type of decay is determined by the isotope, not by the element alone. Carbon-11 has 5 neutrons and carbon-14 has 8, so knowing how carbon-14 decays does not tell us how carbon-11 decays. (Carbon-11 in fact decays by beta-plus emission.)
DIt cannot be tested, since each nucleus chooses its decay type by chance. A student who thinks the type of decay is random picks this. The time of each decay is random, but the type is determined by the isotope, so it can be tested by observing carbon-11 nuclei.
In preparation: 0 of 3 sections compiled and reviewed. The rest show key terms and common mistakes from our question bank until they are.
15.8.A.1 Radioactive decay Fix
Radioactive decay
The spontaneous transformation of an unstable nucleus, in which it emits one or more particles or a photon. Some decay processes emit subatomic particles with properties unlike those of protons, neutrons and electrons.
Alpha particle, α or He²⁺
A helium-4 nucleus: two protons and two neutrons bound together, with no electrons. Charge +2e; nucleon number 4. (In AP Physics 2 only He-4 nuclei are considered.)
Neutrino, ν, and antineutrino, ν̄
Subatomic particles that have no electric charge and negligible mass. A neutrino is emitted in beta-plus decay and an antineutrino in beta-minus decay. Neither is a nucleon.
Neutrino interactions with matter
Neutrinos and antineutrinos interact with matter only through the weak force and the gravitational force, so they interact very little with ordinary matter and nearly all of them pass straight through it.
Positron, e⁺ or β⁺
The antielectron: a particle with the same mass as an electron and the opposite charge, +e. It is emitted in beta-plus decay.
Students often think Everything emitted in radioactive decay is a kind of electromagnetic ray, like light or X-rays, with no mass and no charge. In fact No. Of the emissions in this topic, only gamma rays are electromagnetic radiation (photons). Alpha particles, electrons, positrons, neutrinos and antineutrinos are particles with mass, and all of them except the neutrino and antineutrino carry charge.
Students often think An alpha particle is a helium atom, with two electrons as well as two protons and two neutrons, so it is electrically neutral. In fact No. An alpha particle is a helium-4 nucleus: two protons and two neutrons with no electrons, so it has a charge of +2e (symbol α or He²⁺).
15.8.A.2 Types of radioactive decay Fix
Types of radioactive decay
Nuclei can decay by alpha decay (α), beta-minus decay (β⁻), beta-plus decay (β⁺) and gamma decay (γ). The first three change the proton number; gamma decay changes only the nucleus's energy.
Nucleon number, A
The total number of nucleons (protons plus neutrons) in a nucleus; the upper number in the notation ᴬZ X. The number of neutrons is N = A − Z.
Proton number, Z
The number of protons in a nucleus, which fixes the element and the nuclear charge, +Ze; the lower number in the notation ᴬZ X.
Lepton number
The CED defines lepton number as the number of electrons and neutrinos. For its statement that lepton number is conserved in every nuclear decay to hold, each antiparticle (positron or antineutrino) is counted as −1; this is a counting convention. Lepton number is conserved in every nuclear decay, together with nucleon number and charge: in β⁻ decay the electron (+1) and antineutrino (−1) add to 0, and in β⁺ decay the positron (−1) and neutrino (+1) add to 0.
Conservation laws in nuclear decay
In all nuclear decays the total nucleon number, the total charge and the lepton number are the same after the decay as before. These laws are used to complete or check decay equations.
Alpha decay
Decay in which a nucleus ejects an alpha particle, ⁴₂He. The nucleon number falls by 4 and the proton number by 2 (so the neutron number also falls by 2).
Beta-minus decay, β⁻
Decay in which a neutron in the nucleus changes into a proton, emitting an electron and an antineutrino. The proton number rises by 1, the neutron number falls by 1 and the nucleon number is unchanged.
Beta-plus decay, β⁺
Decay in which a proton in the nucleus changes into a neutron, emitting a positron and a neutrino. The proton number falls by 1, the neutron number rises by 1 and the nucleon number is unchanged.
Gamma decay, γ
Decay in which a nucleus left in an excited state by an alpha or beta decay drops to a lower energy state by emitting a photon (a gamma ray). The proton number and nucleon number are unchanged; the photon's energy equals the energy difference between the two nuclear states.
Students often think Conservation of charge means that charged particles cannot be produced from an uncharged one, so a neutron cannot give rise to a proton and an electron. In fact No. Conservation of charge requires only that the total charge stays the same. A neutron (charge 0) can change into a proton (+e) and an electron (−e) because their charges add to zero.
Students often think When a neutron changes into a proton (or a proton into a neutron), the nucleon number changes, as if the changed nucleon were lost from the nucleus. In fact No. Neutrons and protons are both nucleons, so turning one into the other leaves the number of nucleons unchanged: in both beta-minus and beta-plus decay the nucleon number stays the same.
15.8.A.3 Isotopes and decay type Fix
Isotopes and decay type
Isotopes are nuclei of the same element (same Z) with different numbers of neutrons. Which type of decay a nucleus undergoes is determined by the isotope, not by the element alone: different isotopes of one element may decay in different ways, and some are stable.
Students often think The type of decay is a property of the element, so all radioactive isotopes of one element decay by the same process. In fact No. The type of decay depends on the particular isotope, that is, on its numbers of protons and neutrons, not on the element alone. Two isotopes of one element can decay in different ways, and some isotopes of an element are stable.
Students often think The way a radioactive material decays depends on its conditions, such as its temperature, pressure or chemical state. In fact No. The type of decay is determined by the isotope, a property of the nucleus. Ordinary changes of temperature, pressure or chemical bonding involve the atoms' electrons, not the nucleus, so they do not change which type of decay a nucleus undergoes.
15 more questions. Every wrong answer here is a real mistake students make, and you see why it is wrong as soon as you answer.
Question 1 of 15
The table shows the charge and mass of four particles that can be emitted when nuclei decay. One entry in the table is incorrect. Which row contains the incorrect entry?
Answer and reasoning
ARow 1Correct A positron has charge +e, as listed, but it has the same mass as an electron, about 0.00055 u, not about 1 u. A mass of about 1 u is that of a proton or a neutron.
BRow 2 A student who thinks every nucleon carries charge +e picks this, expecting +4e for the alpha particle. Only its two protons are charged, so +2e is correct, and its mass of about 4 u is also correct.
CRow 3 A student who thinks a neutrino is a kind of neutron picks this, expecting a mass of about 1 u. A neutrino has no charge and negligible mass, as listed.
DRow 4 A student who thinks antiparticles are always charged picks this. An antineutrino, like a neutrino, has no charge and negligible mass, as listed.
Working Correct values: α: +2e, about 4 u; e⁺: +e, mass of an electron (about 0.00055 u); ν and ν̄: 0, negligible. The positron's listed mass (about 1 u, a nucleon's mass) is the error.
How do the electric charge and the mass of an antineutrino (ν̄) compare with those of a neutrino (ν)?
Answer and reasoning
AThe antineutrino carries an electric charge; the neutrino does not. A student who thinks antiparticles are always charged, like the positron, picks this. The antineutrino has no charge, just like the neutrino.
BThey are alike: neither is charged, and each has negligible mass.Correct Neutrinos and antineutrinos both have no electric charge and negligible mass, so in charge and mass they are the same.
CBoth are uncharged, with masses close to that of a neutron. A student who thinks neutrinos are a kind of neutron picks this. Neutrinos and antineutrinos are uncharged, but their masses are negligible, far smaller than a neutron's.
DBoth are photons of gamma radiation, differing only in their energy. A student who thinks every emission from a decaying nucleus is electromagnetic radiation picks this. Neutrinos and antineutrinos are particles, not photons; the photon of a decay is the gamma ray.
Enormous numbers of neutrinos produced by nuclear fusion in the Sun pass through Earth every second, and almost none of them are absorbed or deflected on the way. Which statement best explains this?
Answer and reasoning
AThey are uncharged, and uncharged particles pass through matter freely. A student who thinks any uncharged particle passes through matter picks this. Neutrons and gamma-ray photons are uncharged, yet matter absorbs them; lack of charge alone does not explain the neutrinos' behavior.
BTheir mass is so small that they slip through the gaps between atoms. A student who pictures matter as a sieve picks this. Particles are stopped by the forces they feel, not by their size: beta particles also have very little mass, yet a few millimeters of aluminum stop them.
CThey are long-wavelength electromagnetic waves, which pass through solids. A student who thinks every emission from a nuclear process is an electromagnetic wave picks this. Neutrinos are particles, not electromagnetic waves; they pass through Earth because they interact only through the weak and gravitational forces.
DNo electric or strong forces act on them; only the weak force and gravity do.Correct Neutrinos have no charge, so no electric force acts on them, and they do not feel the strong force that binds nucleons. They interact with matter only through the weak and gravitational forces, which give very little interaction, so almost all of them pass straight through.
A beam of electrons enters the region between two oppositely charged parallel plates with velocity v, as shown, and follows track 3. A beam of positrons then enters with the same velocity. The figure shows four possible tracks, numbered 1 to 4 (not drawn to scale). Which track do the positrons follow?
Answer and reasoning
ATrack 1Correct A positron has the same mass as an electron and the opposite charge, +e. The electric force on it has the same magnitude as on an electron but the opposite direction, so it accelerates just as much, toward the negative plate: its track is the mirror image of the electrons' track.
BTrack 2 A student who thinks a positron has a proton's mass picks this track, which curves the right way but only slightly. A positron has an electron's mass, so the same force gives it the same large acceleration as an electron.
CTrack 3 A student who thinks β⁺ particles are ordinary electrons picks the electrons' own track. A positron's charge is +e, opposite to an electron's, so the force on it is in the opposite direction.
DTrack 4 A student who thinks beta-plus radiation is an electromagnetic ray picks the straight track. Positrons are charged particles, so the electric field between the plates exerts a force on them.
Working Force F = qE: same magnitude for e⁺ and e⁻, opposite direction. Same mass me → same magnitude of acceleration → mirror-image track, curving toward the negative plate.
The chart shows neutron number N against proton number Z. Starting from the nucleus marked with a dot, four arrows (one of them a loop back to the same nucleus) are meant to show the change produced by each of the four types of decay, as labelled. One of the four is drawn incorrectly. Which one?
Answer and reasoning
AArrow 1 A student who thinks alpha decay lowers the proton number by 4 and the nucleon number by 2 picks this. The α arrow correctly goes 2 steps left and 2 steps down: the alpha particle removes 2 protons and 2 neutrons.
BArrow 2Correct In β⁺ decay a proton changes into a neutron, so Z falls by 1 and N rises by 1: the arrow should go one step to the left and one step up. The arrow labelled β⁺ goes one step left with no change in N, the change that losing a proton would make.
CArrow 3 A student who thinks the changed nucleon is lost from the nucleus in beta decay expects β⁻ decay to lower N by 1 and leave Z unchanged, so the diagonal β⁻ arrow looks wrong. (The same belief makes the drawn β⁺ arrow, one step left with N unchanged, look right.) In β⁻ decay a neutron becomes a proton: Z rises by 1 and N falls by 1, exactly as drawn.
DArrow 4 A student who thinks gamma decay changes the nucleus picks this. Gamma decay leaves Z and N unchanged, so a loop back to the same nucleus is correct.
A student proposes that a free neutron decays into a proton and an electron and nothing else: n → p + e⁻. Which conservation law that holds in all nuclear decays would this proposal break?
Answer and reasoning
ACharge, since two charged particles would come from one neutral particle A student who thinks charged particles cannot come from an uncharged one picks this. The charges +e and −e add to zero, the neutron's charge, so charge is conserved.
BNucleon number, since a neutron would be replaced by a proton A student who thinks changing a neutron into a proton changes the nucleon count picks this. Protons and neutrons are both nucleons: one nucleon before, one after.
CLepton number, since the number of electrons and neutrinos would riseCorrect Lepton number counts electrons and neutrinos, with a positron or antineutrino counted as −1. Before the decay it is 0; after n → p + e⁻ it would be +1, from the electron, so lepton number would not be conserved. In the actual decay an antineutrino (−1) is also emitted, so the total stays 0.
DMass, since the proton and electron have less mass than the neutron A student who thinks mass must be conserved picks this. The products of any decay have less mass than the original particle; the difference is released as energy. Mass on its own is not one of the conserved quantities.
A student writes this equation for a decay of carbon-14: ¹⁴₆C → ¹⁴₇N + e⁺ + ν. Which is the best evidence that the equation cannot describe a real decay?
Answer and reasoning
ANucleon number: the total is 14 before the decay but 15 after. A student who counts the positron as a nucleon picks this. The positron and neutrino have nucleon number 0, so there are 14 nucleons on each side.
BLepton number: a positron must be emitted with an antineutrino. A student who pairs the positron with the antineutrino picks this. In beta-plus decay a positron is emitted with a neutrino, as written; the fault in the equation is the charge.
CMass: the products have less mass than the carbon-14 nucleus. A student who thinks mass must be conserved picks this. The products of every decay have less mass than the original nucleus; that loss of mass is the source of the energy released, not a reason the decay is impossible.
DCharge: the total is +6e before the decay but +8e after it.Correct Before: carbon, charge +6e. After: nitrogen +7e plus the positron +e plus the uncharged neutrino, total +8e. Charge is not conserved, so the decay cannot happen as written. (Nucleon number, 14, is balanced, and so is lepton number: positron −1 plus neutrino +1 gives 0.)
Working Charge: 6e → 7e + e + 0 = 8e (not conserved). Nucleon number: 14 → 14 + 0 + 0 (conserved). Lepton number: e⁺ (−1) + ν (+1) = 0 (balanced). So charge is the violated law; the real decay of carbon-14 is ¹⁴₆C → ¹⁴₇N + e⁻ + ν̄.
A radium-226 nucleus, ²²⁶₈₈Ra, undergoes alpha decay. How many neutrons does the resulting nucleus contain?
Answer and reasoning
A138 A student who thinks the alpha particle's charge is +4e subtracts 4 from Z as well as from A, giving N = 222 − 84 = 138, the same as before the decay. The alpha particle has two protons, so Z falls by 2 and N falls by 2.
B136Correct The alpha particle, ⁴₂He, removes 4 nucleons and 2 protons. The new nucleus has A = 226 − 4 = 222 and Z = 88 − 2 = 86, so N = A − Z = 222 − 86 = 136.
C140 A student who exchanges the two changes, taking 2 from A and 4 from Z, gets A = 224 and Z = 84, so N = 140. Alpha decay lowers A by 4 and Z by 2.
D222 A student who takes the nucleon number to be the number of neutrons picks this: 222 is the new nucleus's nucleon number. The number of neutrons is A − Z = 222 − 86 = 136.
Working α = ⁴₂He. A' = 226 − 4 = 222; Z' = 88 − 2 = 86; N' = 222 − 86 = 136. Distractors: Z − 4 → N = 222 − 84 = 138; A − 2, Z − 4 → 224 − 84 = 140; A' reported as N → 222.
Each beta-minus decay of a particular isotope releases the same total amount of energy. However, the emitted electrons are observed to have a range of kinetic energies, from nearly zero up to a maximum value. Which claim is best supported by this observation?
Answer and reasoning
AAnother emitted particle, the antineutrino, carries off the rest of the energy.Correct If the released energy is always the same but the electron's share varies, another product must carry the rest in each decay. In β⁻ decay that product is the antineutrino, which is uncharged and interacts very little with matter, so it escapes unnoticed.
BThe electrons come from different orbits of the atom, which have different energies. A student who thinks beta particles are orbiting electrons picks this. The electrons are emitted by the nucleus, where a neutron changes into a proton; the atom's electron energy levels do not set their energies.
CEnergy is not conserved in beta decay, since mass and energy are converted there. A student who thinks mass-energy conversion suspends energy conservation picks this. Energy is conserved in every decay once mass-energy is included; the missing energy is carried away by the antineutrino.
DThe electrons were already inside the nucleus, each with a different energy. A student who thinks a neutron is a proton and an electron joined together picks this. The nucleus contains no electrons; the electron is produced in the decay, and it shares the released energy with the antineutrino.
Working Fixed total energy released per decay; variable electron kinetic energy → the remainder must go to another emitted product. In β⁻ decay: n → p + e⁻ + ν̄; the antineutrino takes the difference (the recoiling nucleus takes a very small share).
The bar chart shows the numbers of protons and neutrons in a nucleus before and after it undergoes a single radioactive decay. Which particles are emitted in this decay?
Answer and reasoning
AAn electron and an antineutrino A student who has the directions of the beta decays reversed picks this. Emitting an electron (β⁻ decay) turns a neutron into a proton, which would raise the proton number; here it falls.
BOne positron and one antineutrino A student who pairs the positron with the antineutrino picks this. In β⁺ decay the positron is emitted with a neutrino.
CA gamma-ray photon and nothing else A student who thinks gamma decay can change the element picks this. A gamma-ray photon has no charge, so it cannot change the number of protons; here the proton number has changed.
DOne positron and one neutrinoCorrect The number of protons falls from 11 to 10 and the number of neutrons rises from 11 to 12, while the total number of nucleons stays 22: a proton has changed into a neutron. That is β⁺ decay, in which a positron and a neutrino are emitted.
A nucleus containing 15 protons and 15 neutrons undergoes beta-plus decay. How many neutrons does the resulting nucleus contain?
Answer and reasoning
A14 A student who has the directions of the beta decays reversed picks this, turning a neutron into a proton. In β⁺ decay a proton changes into a neutron, so the neutron number rises to 16.
B16Correct In β⁺ decay a proton in the nucleus changes into a neutron, emitting a positron and a neutrino. The new nucleus has 14 protons and 15 + 1 = 16 neutrons; the nucleon number stays 30.
C15 A student who thinks the positron is a proton ejected from the nucleus picks this: losing a proton would leave the neutrons unchanged. The positron has an electron's mass; in β⁺ decay a proton changes into a neutron.
D30 A student who takes the nucleon number to be the number of neutrons picks this: 30 is the nucleon number, unchanged by the decay. The new nucleus has 14 protons, so it has 30 − 14 = 16 neutrons.
Working β⁺: p → n + e⁺ + ν. Z: 15 → 14; N: 15 → 16; A = 30 unchanged. Distractors: n → p (reversed) → N = 14; proton ejected → N = 15; A reported as N → 30.
The energy-level diagram shows a parent nucleus and two energy states of the new nucleus it becomes. The parent nucleus undergoes beta-minus decay to the excited state of the new nucleus, which then emits a gamma-ray photon as it drops to its ground state. What is the frequency of the gamma-ray photon? Use h = 4.14 × 10⁻¹⁵ eV·s.
Answer and reasoning
A1.6 × 10²⁰ HzCorrect The photon carries the energy between the excited state and the ground state of the new nucleus: E = 0.66 MeV − 0 = 0.66 × 10⁶ eV. f = E/h = (0.66 × 10⁶ eV)/(4.14 × 10⁻¹⁵ eV·s) = 1.6 × 10²⁰ Hz.
B1.2 × 10²⁰ Hz A student who thinks the photon is emitted by the parent nucleus as it decays picks this, using the gap from 1.17 MeV to 0.66 MeV, 0.51 MeV. That energy is shared by the electron and the antineutrino of the β⁻ decay; the photon comes afterward, from 0.66 MeV to 0.
C2.8 × 10²⁰ Hz A student who gives the photon all the energy released picks this, using 1.17 MeV. Only the last step, from the excited state at 0.66 MeV to the ground state, produces the photon.
D1.6 × 10¹⁴ Hz A student who divides 0.66 by h without converting MeV to eV picks this. 0.66 MeV = 0.66 × 10⁶ eV, which makes the frequency 10⁶ times larger: 1.6 × 10²⁰ Hz.
Working Gamma transition: excited state (0.66 MeV) → ground state (0). E = 0.66 MeV = 6.6 × 10⁵ eV. f = E/h = 6.6 × 10⁵ eV / 4.14 × 10⁻¹⁵ eV·s = 1.59 × 10²⁰ Hz ≈ 1.6 × 10²⁰ Hz. Distractors: 0.51 MeV → 1.2 × 10²⁰ Hz; 1.17 MeV → 2.8 × 10²⁰ Hz; 0.66 eV → 1.6 × 10¹⁴ Hz.
AThe nucleus becomes a different element as it emits the photon. A student who thinks every type of decay changes the element picks this. The photon carries no charge, so the proton number, and therefore the element, is unchanged.
BIt happens first, preparing the nucleus for an alpha or beta decay. A student who thinks gamma emission comes first picks this. Gamma decay follows an alpha or beta decay that has left the new nucleus in an excited state.
CThe nucleus absorbs a photon and moves to a higher energy state. A student who confuses emission with absorption picks this. In gamma decay the nucleus emits a photon and moves down to a lower energy state.
DThe nucleus loses energy but keeps its proton and nucleon numbers.Correct In gamma decay an excited nucleus emits a photon and drops to a lower energy state. A photon has no charge and no nucleon number, so the proton and nucleon numbers are unchanged; only the nucleus's energy decreases.
The table shows the number of neutrons in each of six isotopes of carbon (each has 6 protons) and how each isotope decays. Which claim is supported by the data in the table?
Answer and reasoning
ACarbon isotopes with more neutrons than the stable ones decay by β⁺. A student who thinks β⁺ decay turns a neutron into a proton expects neutron-rich isotopes to use it and picks this. The table shows carbon-14 and carbon-15, which have extra neutrons, decaying by β⁻.
BEvery unstable isotope of carbon decays by the same process. A student who thinks the decay type belongs to the element picks this. The table shows two processes, β⁺ for carbon-10 and carbon-11 and β⁻ for carbon-14 and carbon-15.
CEach carbon nucleus decays by β⁺ or β⁻, with the type chosen at random. A student who thinks the type of decay is random picks this. The table gives a single decay type for each isotope, and two isotopes are stable, so the type is set by the isotope, not chosen at random.
DCarbon isotopes with more neutrons than the stable ones undergo β⁻ decay.Correct The stable isotopes have 6 and 7 neutrons. The isotopes with more (8 and 9) decay by β⁻, and those with fewer (4 and 5) decay by β⁺. In β⁻ decay a neutron becomes a proton, which suits a nucleus with extra neutrons.
A nucleus has nucleon number A and proton number Z. It undergoes an alpha decay, and the nucleus formed then undergoes a beta-minus decay. Which expression gives the number of neutrons in the final nucleus?
Answer and reasoning
AA − Z − 3Correct After the alpha decay the nucleus has nucleon number A − 4 and proton number Z − 2. In the beta-minus decay a neutron changes into a proton, so the nucleon number stays A − 4 and the proton number becomes Z − 1. Neutrons = (A − 4) − (Z − 1) = A − Z − 3.
BA − Z + 1 A student who exchanges the alpha-decay changes, lowering the proton number by 4 and the nucleon number by 2, picks this. An alpha particle carries 2 protons and 2 neutrons: Z falls by 2 and A by 4.
CA − Z − 1 A student who thinks beta-minus decay changes a proton into a neutron picks this. In beta-minus decay a neutron changes into a proton, so the neutron number falls by 1 and the proton number rises by 1.
DA − Z − 4 A student who counts the emitted electron as a nucleon lowers the nucleon number to A − 5 in the beta-minus decay and picks this. The electron is not a nucleon; the nucleon number stays A − 4.
Working Alpha decay removes 2 protons and 2 neutrons: nucleon number A − 4, proton number Z − 2. Beta-minus decay changes a neutron into a proton: nucleon number A − 4, proton number Z − 1. Neutrons = (A − 4) − (Z − 1) = A − Z − 3. Errors: alpha changes exchanged (Z − 4, A − 2) → A − Z + 1; beta-minus as p → n → A − Z − 1; electron counted as a nucleon (A − 5, Z − 1) → A − Z − 4.
Compiled from the AP Physics 2 Course and Exam Description (effective Fall 2024, 2026 reissue) and our question bank · Specialist review in progress. How these pages are made · Free, no account
