Types of Radioactive Decay - AP Physics 2

1. A nucleus emits a gamma ray during decay. Which statement about the nucleus is correct afterward?
   Answer: Its mass number and atomic number stay the same This question tests understanding of types of radioactive decay. Gamma decay involves an excited nucleus releasing excess energy as a high-energy photon (gamma ray) without changing its nuclear composition. Since no nucleons are added or removed, both mass number A and atomic number Z remain unchanged. The nucleus simply transitions from a higher to lower energy state. Choice D incorrectly suggests mass increases with energy gain, confusing mass-energy equivalence with actual nucleon count. Choice B would indicate beta decay, not gamma. Remember that gamma rays are pure electromagnetic energy with no mass or charge, so they cannot change A or Z.
2. A nucleus changes from $^{210}_{84}\text{Po}$ to $^{206}_{82}\text{Pb}$. Which decay occurs?
   Answer: Alpha decay, emitting $^{4}_{2}\text{He}$ This question tests understanding of types of radioactive decay. The nucleus transforms from Po-210 (Z=84, A=210) to Pb-206 (Z=82, A=206), showing decreases of 2 in atomic number and 4 in mass number. Alpha decay emits a helium-4 nucleus containing 2 protons and 2 neutrons, producing exactly these changes: ΔZ = -2 and ΔA = -4. Beta decays would only change Z by 1 without affecting A, while gamma decay changes neither value. Choice B incorrectly suggests gamma decay can lower mass number, revealing the misconception that photons have mass. The simultaneous decrease of Z by 2 and A by 4 is the unique signature of alpha decay.
3. $^{226}_{88}\text{Ra}$ decays to $^{222}_{86}\text{Rn}$. Which particle must be emitted?
   Answer: An alpha particle, because mass number decreases by 4 and atomic number by 2 This question tests understanding of types of radioactive decay. In alpha decay, the nucleus emits an alpha particle containing 2 protons and 2 neutrons, causing the mass number to decrease by 4 and the atomic number to decrease by 2. Radium-226 (mass 226, atomic number 88) becomes radon-222 (mass 222, atomic number 86), showing exactly these changes: mass decreased by 4 (226-222=4) and atomic number decreased by 2 (88-86=2), confirming alpha particle emission. Choice A incorrectly attributes the atomic number decrease to gamma emission, but gamma rays cannot remove protons from the nucleus since they are massless photons. When analyzing nuclear equations, calculate the differences in mass and atomic numbers to identify the emitted particle.
4. A nucleus emits a particle and its mass number decreases by 4. Which type of decay occurred?
   Answer: Alpha decay, emitting a helium nucleus and decreasing atomic number by 2 This question tests understanding of types of radioactive decay. In alpha decay, the nucleus emits an alpha particle (helium-4 nucleus) containing 2 protons and 2 neutrons, which causes the mass number to decrease by exactly 4 and the atomic number to decrease by 2. The problem states only that mass number decreases by 4, which is the defining characteristic of alpha emission since no other common decay mode removes exactly 4 nucleons. Choice B incorrectly associates beta-minus decay with mass number change, but beta particles are electrons with negligible mass that don't affect the total number of nucleons. When mass number decreases by 4, alpha decay is the only standard radioactive process that produces this change.
5. A nucleus changes from $^{131}_{53}\text{I}$ to $^{131}_{54}\text{Xe}$. Which type of decay occurs?
   Answer: Beta-minus decay, emitting an electron and increasing atomic number by 1 This question tests understanding of types of radioactive decay. In beta-minus decay, a neutron transforms into a proton while emitting an electron and an antineutrino, causing the atomic number to increase by 1 while the mass number remains constant. Iodine-131 (atomic number 53) becomes xenon-131 (atomic number 54) with the same mass number, showing the atomic number increased by 1, which is the signature of beta-minus decay. Choice C incorrectly claims gamma decay changes atomic number, but gamma rays cannot change the number of protons in a nucleus since they are just energy-carrying photons. To recognize beta-minus decay, check if atomic number increases by 1 while mass number stays the same.
6. An unstable nucleus decays by emitting a positron. What happens to the atomic number $Z$ of the daughter nucleus?
   Answer: $Z$ decreases by 1 because a proton becomes a neutron This question tests understanding of types of radioactive decay. A positron is the antiparticle of an electron with positive charge, emitted during beta-plus decay. In this process, a proton converts to a neutron plus a positron (and neutrino), decreasing the atomic number Z by 1. The mass number A remains constant since the total nucleon count doesn't change. Choice A describes beta-minus decay where Z increases, showing confusion between the two beta decay types. Choice C describes alpha decay, not positron emission. To distinguish beta decays, remember: positron emission means a proton becomes a neutron, so Z decreases.
7. An unstable nucleus emits an alpha particle. Compared with the original nucleus, what happens to $A$ and $Z$?
   Answer: $A$ decreases by 4 and $Z$ decreases by 2 This question tests understanding of types of radioactive decay. An alpha particle consists of 2 protons and 2 neutrons (helium-4 nucleus), so when emitted, it removes exactly these nucleons from the parent nucleus. The mass number A decreases by 4 (total nucleons lost) and atomic number Z decreases by 2 (protons lost). This is the defining characteristic of alpha decay. Choice B reverses the changes, showing confusion about alpha particle composition. Choice C suggests only Z changes, which would be beta decay, not alpha. Remember that alpha particles are helium nuclei with specific composition: 2 protons and 2 neutrons.
8. An unstable $^{14}_{6}\text{C}$ nucleus becomes $^{14}_{7}\text{N}$ without changing mass number. Which particle is emitted?
   Answer: A beta-minus particle (electron), increasing atomic number by 1 This question tests understanding of types of radioactive decay. In beta-minus decay, a neutron converts to a proton by emitting an electron (beta particle), increasing the atomic number by 1 while mass number stays constant. Carbon-14 (Z=6, A=14) becomes nitrogen-14 (Z=7, A=14), showing atomic number increases by 1 (6→7) with unchanged mass number (14→14). Alpha decay would decrease both mass and atomic numbers, while gamma decay changes neither. Choice D incorrectly states beta-plus decay increases mass number, revealing the misconception that emitted particles add to nuclear mass rather than being created from existing nucleons. To identify decay type, compare initial and final atomic numbers and mass numbers systematically.
9. A nucleus of $^{210}_{84}\text{Po}$ becomes $^{206}_{82}\text{Pb}$ and emits a particle. Which type of decay occurs?
   Answer: Alpha decay emitting a $^{4}_{2}\text{He}$ nucleus This question tests understanding of types of radioactive decay. In alpha decay, a nucleus emits an alpha particle (helium-4 nucleus), which has 2 protons and 2 neutrons, causing the mass number to decrease by 4 and atomic number to decrease by 2. Here, Po-210 (Z=84, A=210) becomes Pb-206 (Z=82, A=206), showing exactly these changes: mass number drops by 4 (210→206) and atomic number drops by 2 (84→82). Beta decay would only change atomic number by 1, while gamma decay changes neither mass nor atomic number. Choice A incorrectly claims gamma decay changes mass number, revealing confusion about gamma rays being massless photons. When analyzing nuclear decay, always check both mass and atomic number changes to identify the decay type.
10. A nucleus of $^{40}_{19}\text{K}$ becomes $^{40}_{20}\text{Ca}$ with no change in mass number. Which particle is emitted?
    Answer: A beta-minus particle (electron), increasing atomic number by 1 This question tests understanding of types of radioactive decay. In beta-minus decay, a neutron converts to a proton by emitting an electron (beta-minus particle), increasing atomic number by 1 while mass number remains unchanged. Potassium-40 (Z=19, A=40) becomes calcium-40 (Z=20, A=40), showing atomic number increases by 1 (19→20) with constant mass number (40→40). Alpha decay would change both A and Z, while gamma decay changes neither. Choice D incorrectly claims positron emission increases atomic number by 2, confusing both the particle type and magnitude of change in beta decays. Remember: beta-minus increases Z by 1 (neutron→proton), beta-plus decreases Z by 1 (proton→neutron).
11. An excited nucleus $^{60}_{27}\text{Co}^*$ becomes $^{60}_{27}\text{Co}$ with no change in $A$ or $Z$. Which decay occurs?
    Answer: Gamma decay, emitting a photon This question tests understanding of types of radioactive decay. The excited cobalt-60 nucleus (marked with *) becomes ground-state cobalt-60 with no change in mass number (60) or atomic number (27). Gamma decay occurs when an excited nucleus releases energy as a photon without changing its composition. Alpha decay would decrease A by 4 and Z by 2, while beta decays would change Z by 1. Choice C incorrectly claims beta-minus decay increases mass number, revealing a misconception that particle emission always changes A. When a nucleus transitions from excited to ground state with unchanged A and Z, gamma decay is occurring.
12. An excited nucleus emits radiation but remains $^{60}_{27}\text{Co}$ afterward. Which type of decay occurs?
    Answer: Gamma decay, emitting a photon with no change in mass number or atomic number This question tests understanding of types of radioactive decay. In gamma decay, an excited nucleus releases energy by emitting a gamma ray (high-energy photon) without changing its number of protons or neutrons, so both mass number and atomic number remain constant. The problem states the nucleus remains cobalt-60 after emitting radiation, meaning both the mass number (60) and atomic number (27) are unchanged, which is characteristic of gamma decay only. Choice D incorrectly claims gamma decay increases mass number, but photons have no mass and cannot add nucleons to the nucleus. When a nucleus emits radiation but remains the same isotope, it must be gamma decay releasing excess energy.
13. A nucleus changes from $^{14}_{6}\text{C}$ to $^{14}_{7}\text{N}$. Which particle is emitted in this decay?
    Answer: An electron (beta-minus particle) This question tests understanding of types of radioactive decay. Carbon-14 transforms to nitrogen-14, where the mass number stays at 14 but the atomic number increases from 6 to 7. In beta-minus decay, a neutron converts to a proton plus an electron, increasing Z by 1 while keeping A constant. The emitted electron (beta-minus particle) carries away the negative charge. Alpha decay would decrease both A and Z, while gamma decay changes neither. Choice D incorrectly suggests neutron emission increases atomic number, showing confusion about how neutrons affect nuclear composition. When mass number stays constant but atomic number changes by 1, identify whether Z increases (beta-minus) or decreases (beta-plus).
14. A nucleus emits an electron and becomes a different element with the same mass number. Which decay is occurring?
    Answer: Beta-minus decay, emitting an electron and increasing atomic number by 1 This question tests understanding of types of radioactive decay. In beta-minus decay, a neutron converts to a proton while emitting an electron (beta particle), causing the atomic number to increase by 1 while the mass number remains constant since the total nucleon count doesn't change. The problem states an electron is emitted and the nucleus becomes a different element (higher atomic number) with the same mass number, which perfectly describes beta-minus decay. Choice B incorrectly suggests alpha decay keeps mass number constant, but alpha emission always decreases mass number by 4 due to the loss of 4 nucleons. To identify beta-minus decay, look for electron emission coupled with atomic number increase and constant mass number.
15. A nucleus changes from $^{22}_{11}\text{Na}$ to $^{22}_{10}\text{Ne}$. Which type of decay occurs?
    Answer: Beta-plus decay, emitting a positron This question tests understanding of types of radioactive decay. Sodium-22 changes to neon-22, where mass number remains 22 but atomic number decreases from 11 to 10. In beta-plus decay, a proton converts to a neutron plus a positron, decreasing Z by 1 while keeping A constant. The emitted positron (antimatter electron) carries away the positive charge. Beta-minus decay would increase Z, alpha decay would change both A and Z, and gamma decay changes neither. Choice B incorrectly suggests gamma decay changes mass number, showing confusion about photon emission effects. To distinguish beta decays, check whether atomic number increases (beta-minus) or decreases (beta-plus).
16. An excited $^{60}_{27}\text{Co}^*$ nucleus becomes $^{60}_{27}\text{Co}$ with unchanged $A$ and $Z$. Which decay occurs?
    Answer: Gamma decay, emitting a photon This question tests understanding of types of radioactive decay. The excited Co-60 nucleus (indicated by the asterisk) becomes ground-state Co-60, with both atomic number (27) and mass number (60) remaining unchanged. Gamma decay occurs when an excited nucleus releases energy as a photon without changing its composition, making this the only decay that preserves both Z and A. Alpha decay would reduce both numbers, while beta decay would change Z. Choice D incorrectly suggests gamma decay can decrease mass number, revealing the misconception that photons carry mass and affect nucleon count. When a nucleus transitions from excited to ground state with no change in Z or A, this uniquely identifies gamma decay.
17. A nucleus changes from $^{210}_{84}\text{Po}$ to $^{206}_{82}\text{Pb}$. Which particle is emitted in this decay?
    Answer: A helium nucleus (alpha particle) This question tests understanding of types of radioactive decay. Polonium-210 changes to lead-206, showing mass number decreases from 210 to 206 (by 4) and atomic number decreases from 84 to 82 (by 2). These changes match alpha decay perfectly, where a helium nucleus (2 protons, 2 neutrons) is emitted. Beta decays would only change Z by 1 while keeping A constant, and gamma decay changes neither value. Choice B incorrectly suggests gamma rays reduce mass number, confusing energy emission with particle emission. When both A and Z decrease by 4 and 2 respectively, alpha decay is the only possibility.
18. A nucleus of $^{226}_{88}\text{Ra}$ becomes $^{222}_{86}\text{Rn}$. Which type of decay occurs?
    Answer: Alpha decay emitting a $^{4}_{2}\text{He}$ nucleus, decreasing atomic number by 2 This question tests understanding of types of radioactive decay. In alpha decay, a nucleus emits an alpha particle (helium-4 nucleus) containing 2 protons and 2 neutrons, decreasing mass number by 4 and atomic number by 2. Radium-226 (Z=88, A=226) becomes radon-222 (Z=86, A=222), showing mass number decreases by 4 (226→222) and atomic number decreases by 2 (88→86). Beta decays only change Z by 1, while gamma decay changes neither A nor Z. Choice C incorrectly attributes mass number change to gamma decay, revealing confusion about photons being massless particles that cannot alter nuclear composition. When both A decreases by 4 and Z decreases by 2, alpha decay is the only explanation.
19. A nucleus of $^{22}_{11}\text{Na}$ becomes $^{22}_{10}\text{Ne}$ with unchanged mass number. Which type of decay occurs?
    Answer: Beta-plus decay emitting a positron, decreasing atomic number by 1 This question tests understanding of types of radioactive decay. In beta-plus decay (positron emission), a proton converts to a neutron by emitting a positron, decreasing the atomic number by 1 while mass number remains constant. Sodium-22 (Z=11, A=22) becomes neon-22 (Z=10, A=22), showing atomic number decreases by 1 (11→10) with unchanged mass number (22→22). Beta-minus decay would increase atomic number, while alpha decay would change both mass and atomic numbers. Choice B incorrectly claims beta-minus decay decreases atomic number, revealing confusion about the direction of charge change in beta decays. Remember that beta-plus decreases Z (proton lost) while beta-minus increases Z (proton gained).
20. An unstable $^{131}_{53}\text{I}$ nucleus becomes $^{131}_{54}\text{Xe}$. Which type of decay occurs?
    Answer: Beta-minus decay emitting an electron, increasing atomic number by 1 This question tests understanding of types of radioactive decay. In beta-minus decay, a neutron transforms into a proton by emitting an electron, increasing atomic number by 1 while mass number stays constant. Iodine-131 (Z=53, A=131) becomes xenon-131 (Z=54, A=131), showing atomic number increases by 1 (53→54) with unchanged mass number (131→131). Alpha decay would decrease both numbers, while gamma decay changes neither. Choice B incorrectly suggests gamma decay increases atomic number, revealing the misconception that photon emission can change nuclear charge. When mass number is constant but atomic number increases by 1, beta-minus decay is the only possibility.

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