Interpret Nuclear Equations
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Chemistry › Interpret Nuclear Equations
In beta decay, a nucleus emits an electron ($^{0}{-1}\text{e}$). If $$^{A}{Z}\text{X} \rightarrow ^{A}{Z+1}\text{Y} + ^{0}{-1}\text{e},$$ what happens to the mass number $A$?
It decreases by 4.
It stays the same.
It decreases by 1.
It increases by 1.
Explanation
This question tests your ability to read and interpret nuclear equations that show how nuclei transform during fission, fusion, or radioactive decay, including identifying particles emitted and products formed. Nuclear equations use special notation where each nucleus or particle is written with its element symbol, mass number (superscript, total protons + neutrons), and sometimes atomic number (subscript, number of protons): for example, $^{238}\text{U}$ represents uranium-238 with mass number 238 and atomic number 92 (uranium always has 92 protons). The equation shows what happens: $^{238}\text{U} \rightarrow ^{234}\text{Th} + ^4\text{He}$ means uranium-238 decays to thorium-234 (mass 234, atomic 90) plus an alpha particle ($^4\text{He}$, which is a helium nucleus with mass 4, atomic 2). In nuclear equations, both mass numbers and atomic numbers are conserved (the sums on left equal sums on right): check 238 = 234 + 4 ✓ and 92 = 90 + 2 ✓. Common particles: alpha ($^4\text{He}$), beta ($^{0}{-1}\text{e}$, electron), neutron ($^1\text{n}$), proton ($^1\text{H}$). In beta decay like $^{A}{Z}\text{X} \rightarrow ^{A}{Z+1}\text{Y} + ^{0}{-1}\text{e}$, the mass number A remains unchanged because the emitted beta particle (electron) has negligible mass (0), so A = A + 0. Choice C correctly interprets the nuclear equation by stating that the mass number stays the same. Choice D (decreases by 4) fails as a distractor because that describes alpha decay, not beta, where mass drops by 4. Reading nuclear equations step-by-step: (1) Identify what's on the left (reactant nucleus/nuclei) and right (product nucleus/nuclei and particles). (2) Check conservation: add mass numbers on left, add on right, should equal. Add atomic numbers on left, add on right, should equal. This tells you the equation is valid. (3) Identify unknowns: if you see X in equation, use conservation to find it. Example: $^{226}\text{Ra} \rightarrow ^{222}\text{Rn} + \text{X}$. Mass: 226 = 222 + ? → X has mass 4. Atomic: 88 = 86 + ? → X has atomic 2. So X is $^4_2\text{He}$ (alpha particle). (4) Classify process: one splitting (fission), two combining (fusion), or one emitting particle (decay). The pattern reveals process type! Common particle recognition: if mass drops by 4 and atomic by 2 → alpha emitted ($^4\text{He}$). If atomic number increases by 1 with no mass change → beta emitted (electron, $^{0}_{-1}\text{e}$). If just gamma (energy), no mass or atomic change. If neutrons involved ($^1\text{n}$) and large nucleus splits → fission. If light nuclei combine → fusion. These patterns repeat across nuclear chemistry, so recognizing them once helps with all nuclear equations! Nuclear vs chemical equations: CHEMICAL equations balance atom counts using coefficients (2H2 + O2 → 2H2O keeps atoms same type, just rearranged). NUCLEAR equations balance mass and atomic numbers, but atoms actually CHANGE into different elements (uranium becomes thorium, carbon becomes nitrogen)—this is the key difference! Nuclear changes transform elements, chemical changes only rearrange them. Keep up the fantastic progress!
A nucleus undergoes beta (beta-minus) decay: $$^{131}{53}\mathrm{I} \rightarrow ,^{131}{54}\mathrm{Xe} + ,^{0}_{-1}\mathrm{e}.$$ What changes in the nucleus during this decay?
Mass number decreases by 4 and atomic number decreases by 2
Mass number increases by 1 while atomic number stays the same
Atomic number decreases by 1 while mass number stays the same
Atomic number increases by 1 while mass number stays the same
Explanation
This question tests your ability to read and interpret nuclear equations that show how nuclei transform during fission, fusion, or radioactive decay, including identifying particles emitted and products formed. Nuclear equations use special notation where each nucleus or particle is written with its element symbol, mass number (superscript, total protons + neutrons), and sometimes atomic number (subscript, number of protons): for example, ²³⁸U represents uranium-238 with mass number 238 and atomic number 92 (uranium always has 92 protons). The equation shows what happens: ²³⁸U → ²³⁴Th + ⁴He means uranium-238 decays to thorium-234 (mass 234, atomic 90) plus an alpha particle (⁴He, which is a helium nucleus with mass 4, atomic 2). In nuclear equations, both mass numbers and atomic numbers are conserved (the sums on left equal sums on right): check 238 = 234 + 4 ✓ and 92 = 90 + 2 ✓. Common particles: alpha (⁴He), beta (⁰₋₁e, electron), neutron (¹n), proton (¹H). In this beta-minus decay, ¹³¹₅₃I → ¹³¹₅₄Xe + ⁰₋₁e, the mass number remains 131 while the atomic number increases from 53 to 54, as a neutron turns into a proton with electron emission. Choice B correctly interprets the nuclear equation by describing the atomic number increase by 1 with unchanged mass. A distractor like choice A describes alpha decay instead, which decreases mass by 4 and atomic by 2—beta decay doesn't reduce mass, so always note the 'no mass change' clue. Reading nuclear equations step-by-step: (1) Identify what's on the left (reactant nucleus/nuclei) and right (product nucleus/nuclei and particles). (2) Check conservation: add mass numbers on left, add on right, should equal. Add atomic numbers on left, add on right, should equal. This tells you the equation is valid. (3) Identify unknowns: if you see X in equation, use conservation to find it. Example: ²²⁶Ra → ²²²Rn + X. Mass: 226 = 222 + ? → X has mass 4. Atomic: 88 = 86 + ? → X has atomic 2. So X is ⁴₂He (alpha particle). (4) Classify process: one splitting (fission), two combining (fusion), or one emitting particle (decay). The pattern reveals process type! Common particle recognition: if mass drops by 4 and atomic by 2 → alpha emitted (⁴He). If atomic number increases by 1 with no mass change → beta emitted (electron, ⁰₋₁e). If just gamma (energy), no mass or atomic change. If neutrons involved (¹n) and large nucleus splits → fission. If light nuclei combine → fusion. These patterns repeat across nuclear chemistry, so recognizing them once helps with all nuclear equations! Nuclear vs chemical equations: CHEMICAL equations balance atom counts using coefficients (2H2 + O2 → 2H2O keeps atoms same type, just rearranged). NUCLEAR equations balance mass and atomic numbers, but atoms actually CHANGE into different elements (uranium becomes thorium, carbon becomes nitrogen)—this is the key difference! Nuclear changes transform elements, chemical changes only rearrange them. Excellent observation of those changes!
Which product nucleus forms in the beta decay $$^{14}{6}\text{C} \rightarrow \text{(product)} + ^{0}{-1}\text{e}?$$
$^{10}_{4}\text{Be}$
$^{14}_{5}\text{B}$
$^{13}_{7}\text{N}$
$^{14}_{7}\text{N}$
Explanation
This question tests your ability to read and interpret nuclear equations that show how nuclei transform during fission, fusion, or radioactive decay, including identifying particles emitted and products formed. Nuclear equations use special notation where each nucleus or particle is written with its element symbol, mass number (superscript, total protons + neutrons), and sometimes atomic number (subscript, number of protons): for example, $$^{238}{92}\text{U}$$ represents uranium-238 with mass number 238 and atomic number 92 (uranium always has 92 protons). The equation shows what happens: $$^{238}{92}\text{U} \rightarrow ^{234}{90}\text{Th} + ^{4}{2}\text{He}$$ means uranium-238 decays to thorium-234 (mass 234, atomic 90) plus an alpha particle ($$^{4}{2}\text{He}$$, which is a helium nucleus with mass 4, atomic 2). In nuclear equations, both mass numbers and atomic numbers are conserved (the sums on left equal sums on right): check 238 = 234 + 4 ✓ and 92 = 90 + 2 ✓. Common particles: alpha ($$^{4}{2}\text{He}$$), beta ($$^{0}{-1}\text{e}$$, electron), neutron ($$^{1}{0}\text{n}$$), proton ($$^{1}{1}\text{H}$$). In beta decay of $$^{14}{6}\text{C} \rightarrow$$ product + $$^{0}{-1}\text{e}$$, mass stays 14 (14=14+0) and atomic increases to 7 (6=7-1), so the product is $$^{14}{7}\text{N}$$. Choice C correctly interprets the nuclear equation by identifying the product nucleus as $$^{14}{7}\text{N}$$. Choice B ($$^{13}{7}\text{N}$$) fails as a distractor because it has mass 13, but beta decay doesn't change mass number. Reading nuclear equations step-by-step: (1) Identify what's on the left (reactant nucleus/nuclei) and right (product nucleus/nuclei and particles). (2) Check conservation: add mass numbers on left, add on right, should equal. Add atomic numbers on left, add on right, should equal. This tells you the equation is valid. (3) Identify unknowns: if you see X in equation, use conservation to find it. Example: $$^{226}{88}\text{Ra} \rightarrow ^{222}{86}\text{Rn} + \text{X}$$. Mass: 226 = 222 + ? → X has mass 4. Atomic: 88 = 86 + ? → X has atomic 2. So X is $$^{4}{2}\text{He}$$ (alpha particle). (4) Classify process: one splitting (fission), two combining (fusion), or one emitting particle (decay). The pattern reveals process type! Common particle recognition: if mass drops by 4 and atomic by 2 → alpha emitted ($$^{4}{2}\text{He}$$). If atomic number increases by 1 with no mass change → beta emitted (electron, $$^{0}{-1}\text{e}$$). If just gamma (energy), no mass or atomic change. If neutrons involved ($$^{1}{0}\text{n}$$) and large nucleus splits → fission. If light nuclei combine → fusion. These patterns repeat across nuclear chemistry, so recognizing them once helps with all nuclear equations! Nuclear vs chemical equations: CHEMICAL equations balance atom counts using coefficients (2H2 + O2 → 2H2O keeps atoms same type, just rearranged). NUCLEAR equations balance mass and atomic numbers, but atoms actually CHANGE into different elements (uranium becomes thorium, carbon becomes nitrogen)—this is the key difference! Nuclear changes transform elements, chemical changes only rearrange them. Awesome job on beta decay!
The nuclear equation $$^{14}{6}\text{C} \rightarrow ^{14}{7}\text{N} + ^{0}_{-1}\text{e}$$ shows which type of radioactive decay?
Gamma emission
Nuclear fusion
Beta ($\beta^{-}$) decay
Alpha decay
Explanation
This question tests your ability to read and interpret nuclear equations that show how nuclei transform during fission, fusion, or radioactive decay, including identifying particles emitted and products formed. Nuclear equations use special notation where each nucleus or particle is written with its element symbol, mass number (superscript, total protons + neutrons), and sometimes atomic number (subscript, number of protons): for example, $^{238}\text{U}$ represents uranium-238 with mass number 238 and atomic number 92 (uranium always has 92 protons). The equation shows what happens: $^{238}\text{U} \rightarrow ^{234}\text{Th} + ^{4}\text{He}$ means uranium-238 decays to thorium-234 (mass 234, atomic 90) plus an alpha particle ($^{4}\text{He}$, which is a helium nucleus with mass 4, atomic 2). In nuclear equations, both mass numbers and atomic numbers are conserved (the sums on left equal sums on right): check 238 = 234 + 4 ✓ and 92 = 90 + 2 ✓. Common particles: alpha ($^{4}\text{He}$), beta ($^{0}{-1}\text{e}$, electron), neutron ($^{1}\text{n}$), proton ($^{1}\text{H}$). Here, $^{14}{6}\text{C} \rightarrow ^{14}{7}\text{N} + ^{0}{-1}\text{e}$ shows mass stays 14 (14=14+0) and atomic increases from 6 to 7 (6=7 + (-1)), with an electron emitted, which is the signature of beta decay where a neutron turns into a proton. Choice B correctly interprets the nuclear equation by recognizing this as beta ($\beta^{-}$) decay due to the atomic number increase and beta particle emission. A distractor like choice A (alpha decay) fails because alpha decay decreases mass by 4 and atomic by 2, not matching this equation's unchanged mass and increased atomic number. Reading nuclear equations step-by-step: (1) Identify what's on the left (reactant nucleus/nuclei) and right (product nucleus/nuclei and particles). (2) Check conservation: add mass numbers on left, add on right, should equal. Add atomic numbers on left, add on right, should equal. This tells you the equation is valid. (3) Identify unknowns: if you see X in equation, use conservation to find it. Example: $^{226}\text{Ra} \rightarrow ^{222}\text{Rn} + \text{X}$. Mass: 226 = 222 + ? → X has mass 4. Atomic: 88 = 86 + ? → X has atomic 2. So X is $^{4}{2}\text{He}$ (alpha particle). (4) Classify process: one splitting (fission), two combining (fusion), or one emitting particle (decay). The pattern reveals process type! Common particle recognition: if mass drops by 4 and atomic by 2 → alpha emitted ($^{4}{2}\text{He}$). If atomic number increases by 1 with no mass change → beta emitted (electron, $^{0}_{-1}\text{e}$). If just gamma (energy), no mass or atomic change. If neutrons involved ($^{1}\text{n}$) and large nucleus splits → fission. If light nuclei combine → fusion. These patterns repeat across nuclear chemistry, so recognizing them once helps with all nuclear equations! Nuclear vs chemical equations: CHEMICAL equations balance atom counts using coefficients (2H2 + O2 → 2H2O keeps atoms same type, just rearranged). NUCLEAR equations balance mass and atomic numbers, but atoms actually CHANGE into different elements (uranium becomes thorium, carbon becomes nitrogen)—this is the key difference! Nuclear changes transform elements, chemical changes only rearrange them. You're doing great—keep identifying those patterns!
In the fusion equation $$^{2}{1}\text{H} + ^{2}{1}\text{H} \rightarrow ^{3}_{2}\text{He} + X$$, which particle must $X$ be to conserve mass number and atomic number?
$^{0}_{-1}\text{e}$ (beta particle)
$^{1}_{0}\text{n}$ (neutron)
$^{1}_{1}\text{H}$ (proton)
$^{4}_{2}\text{He}$ (alpha particle)
Explanation
This question tests your ability to read and interpret nuclear equations that show how nuclei transform during fission, fusion, or radioactive decay, including identifying particles emitted and products formed. Nuclear equations use special notation where each nucleus or particle is written with its element symbol, mass number (superscript, total protons + neutrons), and sometimes atomic number (subscript, number of protons): for example, $$^{238}{92}\text{U}$$ represents uranium-238 with mass number 238 and atomic number 92 (uranium always has 92 protons). The equation shows what happens: $$^{238}{92}\text{U} \rightarrow ^{234}{90}\text{Th} + ^{4}{2}\text{He}$$ means uranium-238 decays to thorium-234 (mass 234, atomic 90) plus an alpha particle ($$^{4}{2}\text{He}$$, which is a helium nucleus with mass 4, atomic 2). In nuclear equations, both mass numbers and atomic numbers are conserved (the sums on left equal sums on right): check 238 = 234 + 4 ✓ and 92 = 90 + 2 ✓. Common particles: alpha ($$^{4}{2}\text{He}$$), beta ($$^{0}{-1}\text{e}$$, electron), neutron ($$^{1}{0}\text{n}$$), proton ($$^{1}{1}\text{H}$$). For fusion $$^{2}{1}\text{H} + ^{2}{1}\text{H} \rightarrow ^{3}{2}\text{He} + X$$, masses balance as 2+2=3+1 and atomics as 1+1=2+0, so X must be $$^{1}{0}\text{n}$$, a neutron. Choice B correctly interprets the nuclear equation by identifying X as a neutron to conserve both mass and atomic numbers. Choice D (alpha particle) fails because an alpha has mass 4 and atomic 2, which would unbalance the equation (left mass 4, right 3+4=7). Reading nuclear equations step-by-step: (1) Identify what's on the left (reactant nucleus/nuclei) and right (product nucleus/nuclei and particles). (2) Check conservation: add mass numbers on left, add on right, should equal. Add atomic numbers on left, add on right, should equal. This tells you the equation is valid. (3) Identify unknowns: if you see X in equation, use conservation to find it. Example: $$^{226}{88}\text{Ra} \rightarrow ^{222}{86}\text{Rn} + X$$. Mass: 226 = 222 + ? → X has mass 4. Atomic: 88 = 86 + ? → X has atomic 2. So X is $$^{4}{2}\text{He}$$ (alpha particle). (4) Classify process: one splitting (fission), two combining (fusion), or one emitting particle (decay). The pattern reveals process type! Common particle recognition: if mass drops by 4 and atomic by 2 → alpha emitted ($$^{4}{2}\text{He}$$). If atomic number increases by 1 with no mass change → beta emitted (electron, $$^{0}{-1}\text{e}$$). If just gamma (energy), no mass or atomic change. If neutrons involved ($$^{1}_{0}\text{n}$$) and large nucleus splits → fission. If light nuclei combine → fusion. These patterns repeat across nuclear chemistry, so recognizing them once helps with all nuclear equations! Nuclear vs chemical equations: CHEMICAL equations balance atom counts using coefficients (2H2 + O2 → 2H2O keeps atoms same type, just rearranged). NUCLEAR equations balance mass and atomic numbers, but atoms actually CHANGE into different elements (uranium becomes thorium, carbon becomes nitrogen)—this is the key difference! Nuclear changes transform elements, chemical changes only rearrange them. You're a fusion expert now!
The nuclear equation $$^{226}{88}\text{Ra} \rightarrow ^{222}{86}\text{Rn} + ^{4}_{2}\text{He}$$ is an example of which process?
Fission
Beta decay
Alpha decay
Fusion
Explanation
This question tests your ability to read and interpret nuclear equations that show how nuclei transform during fission, fusion, or radioactive decay, including identifying particles emitted and products formed. Nuclear equations use special notation where each nucleus or particle is written with its element symbol, mass number (superscript, total protons + neutrons), and sometimes atomic number (subscript, number of protons): for example, $ ^{238}\text{U} $ represents uranium-238 with mass number 238 and atomic number 92 (uranium always has 92 protons). The equation shows what happens: $ ^{238}\text{U} \rightarrow ^{234}\text{Th} + ^4\text{He} $ means uranium-238 decays to thorium-234 (mass 234, atomic 90) plus an alpha particle ($ ^4\text{He} $, which is a helium nucleus with mass 4, atomic 2). In nuclear equations, both mass numbers and atomic numbers are conserved (the sums on left equal sums on right): check $ 238 = 234 + 4 \checkmark $ and $ 92 = 90 + 2 \checkmark $. Common particles: alpha ($ ^4\text{He} $), beta ($ ^0_{-1}\text{e} $, electron), neutron ($ ^1\text{n} $), proton ($ ^1\text{H} $). The equation $ ^{226}{88}\text{Ra} \rightarrow ^{222}{86}\text{Rn} + ^4_2\text{He} $ shows a single nucleus emitting an alpha particle, with mass decreasing by 4 (226-4=222) and atomic by 2 (88-2=86), typical of alpha decay. Choice B correctly interprets the nuclear equation by recognizing this as alpha decay. Choice A (beta decay) fails as a distractor because beta decay keeps mass the same and increases atomic number by 1, not decreasing both like here. Reading nuclear equations step-by-step: (1) Identify what's on the left (reactant nucleus/nuclei) and right (product nucleus/nuclei and particles). (2) Check conservation: add mass numbers on left, add on right, should equal. Add atomic numbers on left, add on right, should equal. This tells you the equation is valid. (3) Identify unknowns: if you see X in equation, use conservation to find it. Example: $ ^{226}\text{Ra} \rightarrow ^{222}\text{Rn} + \text{X} $. Mass: $ 226 = 222 + ? \rightarrow \text{X has mass 4} $. Atomic: $ 88 = 86 + ? \rightarrow \text{X has atomic 2} $. So X is $ ^4_2\text{He} $ (alpha particle). (4) Classify process: one splitting (fission), two combining (fusion), or one emitting particle (decay). The pattern reveals process type! Common particle recognition: if mass drops by 4 and atomic by 2 $ \rightarrow $ alpha emitted ($ ^4\text{He} $). If atomic number increases by 1 with no mass change $ \rightarrow $ beta emitted (electron, $ ^0_{-1}\text{e} $). If just gamma (energy), no mass or atomic change. If neutrons involved ($ ^1\text{n} $) and large nucleus splits $ \rightarrow $ fission. If light nuclei combine $ \rightarrow $ fusion. These patterns repeat across nuclear chemistry, so recognizing them once helps with all nuclear equations! Nuclear vs chemical equations: CHEMICAL equations balance atom counts using coefficients (2H2 + O2 $ \rightarrow $ 2H2O keeps atoms same type, just rearranged). NUCLEAR equations balance mass and atomic numbers, but atoms actually CHANGE into different elements (uranium becomes thorium, carbon becomes nitrogen)—this is the key difference! Nuclear changes transform elements, chemical changes only rearrange them. You're building strong skills here!
A nucleus undergoes alpha decay. If the original nucleus is $$^{238}_{92}\text{U},$$ what are the mass number and atomic number of the daughter nucleus (the nucleus left behind)?
Mass 236, atomic 92
Mass 234, atomic 90
Mass 238, atomic 91
Mass 242, atomic 94
Explanation
This question tests your ability to read and interpret nuclear equations that show how nuclei transform during fission, fusion, or radioactive decay, including identifying particles emitted and products formed. Nuclear equations use special notation where each nucleus or particle is written with its element symbol, mass number (superscript, total protons + neutrons), and sometimes atomic number (subscript, number of protons): for example, ²³⁸U represents uranium-238 with mass number 238 and atomic number 92 (uranium always has 92 protons). The equation shows what happens: ²³⁸U → ²³⁴Th + ⁴He means uranium-238 decays to thorium-234 (mass 234, atomic 90) plus an alpha particle (⁴He, which is a helium nucleus with mass 4, atomic 2). In nuclear equations, both mass numbers and atomic numbers are conserved (the sums on left equal sums on right): check 238 = 234 + 4 ✓ and 92 = 90 + 2 ✓. Common particles: alpha (⁴He), beta (⁰₋₁e, electron), neutron (¹n), proton (¹H). For alpha decay of ²³⁸₉₂U, the daughter nucleus loses mass 4 (238-4=234) and atomic 2 (92-2=90), resulting in mass 234, atomic 90. Choice C correctly interprets the nuclear equation by stating the daughter has mass 234 and atomic 90. Choice D (mass 236, atomic 92) fails because it subtracts only 2 from mass without accounting for alpha's full mass 4 and atomic 2. Reading nuclear equations step-by-step: (1) Identify what's on the left (reactant nucleus/nuclei) and right (product nucleus/nuclei and particles). (2) Check conservation: add mass numbers on left, add on right, should equal. Add atomic numbers on left, add on right, should equal. This tells you the equation is valid. (3) Identify unknowns: if you see X in equation, use conservation to find it. Example: ²²⁶Ra → ²²²Rn + X. Mass: 226 = 222 + ? → X has mass 4. Atomic: 88 = 86 + ? → X has atomic 2. So X is ⁴₂He (alpha particle). (4) Classify process: one splitting (fission), two combining (fusion), or one emitting particle (decay). The pattern reveals process type! Common particle recognition: if mass drops by 4 and atomic by 2 → alpha emitted (⁴He). If atomic number increases by 1 with no mass change → beta emitted (electron, ⁰₋₁e). If just gamma (energy), no mass or atomic change. If neutrons involved (¹n) and large nucleus splits → fission. If light nuclei combine → fusion. These patterns repeat across nuclear chemistry, so recognizing them once helps with all nuclear equations! Nuclear vs chemical equations: CHEMICAL equations balance atom counts using coefficients (2H2 + O2 → 2H2O keeps atoms same type, just rearranged). NUCLEAR equations balance mass and atomic numbers, but atoms actually CHANGE into different elements (uranium becomes thorium, carbon becomes nitrogen)—this is the key difference! Nuclear changes transform elements, chemical changes only rearrange them. Terrific verification of alpha decay!
In the nuclear equation $$^{238}{92}\text{U} \rightarrow ^{234}{90}\text{Th} + X$$, what particle is represented by $X$?
$^{1}_{0}\text{n}$ (neutron)
$^{0}_{-1}\text{e}$ (beta particle)
$^{1}_{1}\text{H}$ (proton)
$^{4}_{2}\text{He}$ (alpha particle)
Explanation
This question tests your ability to read and interpret nuclear equations that show how nuclei transform during fission, fusion, or radioactive decay, including identifying particles emitted and products formed. Nuclear equations use special notation where each nucleus or particle is written with its element symbol, mass number (superscript, total protons + neutrons), and sometimes atomic number (subscript, number of protons): for example, $$^{238}{92}\text{U}$$ represents uranium-238 with mass number 238 and atomic number 92 (uranium always has 92 protons). The equation shows what happens: $$^{238}{92}\text{U} \rightarrow ^{234}{90}\text{Th} + ^{4}{2}\text{He}$$ means uranium-238 decays to thorium-234 (mass 234, atomic 90) plus an alpha particle ($$^{4}{2}\text{He}$$, which is a helium nucleus with mass 4, atomic 2). In nuclear equations, both mass numbers and atomic numbers are conserved (the sums on left equal sums on right): check $$238 = 234 + 4$$ ✓ and $$92 = 90 + 2$$ ✓. Common particles: alpha ($$^{4}{2}\text{He}$$), beta ($$^{0}{-1}\text{e}$$, electron), neutron ($$^{1}{0}\text{n}$$), proton ($$^{1}{1}\text{H}$$). In this case, for $$^{238}{92}\text{U} \rightarrow ^{234}{90}\text{Th} + X$$, subtract to find X: mass 238-234=4, atomic 92-90=2, so X is $$^{4}{2}\text{He}$$, an alpha particle. Choice C correctly interprets the nuclear equation by properly identifying the particle as an alpha particle based on conservation laws. A common distractor like choice A (beta particle) fails because a beta would change atomic number by +1 without matching the mass drop of 4. Reading nuclear equations step-by-step: (1) Identify what's on the left (reactant nucleus/nuclei) and right (product nucleus/nuclei and particles). (2) Check conservation: add mass numbers on left, add on right, should equal. Add atomic numbers on left, add on right, should equal. This tells you the equation is valid. (3) Identify unknowns: if you see X in equation, use conservation to find it. Example: $$^{226}{88}\text{Ra} \rightarrow ^{222}{86}\text{Rn} + X$$. Mass: 226 = 222 + ? → X has mass 4. Atomic: 88 = 86 + ? → X has atomic 2. So X is $$^{4}{2}\text{He}$$ (alpha particle). (4) Classify process: one splitting (fission), two combining (fusion), or one emitting particle (decay). The pattern reveals process type! Common particle recognition: if mass drops by 4 and atomic by 2 → alpha emitted ($$^{4}{2}\text{He}$$). If atomic number increases by 1 with no mass change → beta emitted (electron, $$^{0}{-1}\text{e}$$). If just gamma (energy), no mass or atomic change. If neutrons involved ($$^{1}{0}\text{n}$$) and large nucleus splits → fission. If light nuclei combine → fusion. These patterns repeat across nuclear chemistry, so recognizing them once helps with all nuclear equations! Nuclear vs chemical equations: CHEMICAL equations balance atom counts using coefficients ($$2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$$, keeps atoms same type, just rearranged). NUCLEAR equations balance mass and atomic numbers, but atoms actually CHANGE into different elements (uranium becomes thorium, carbon becomes nitrogen)—this is the key difference! Nuclear changes transform elements, chemical changes only rearrange them. Keep practicing these, and you'll master nuclear equations in no time!
A nucleus undergoes beta decay: $$^{131}{53}\mathrm{I} \rightarrow X + {}^{0}{-1}\mathrm{e}.$$ What nucleus is $X$?
$^{135}_{55}\mathrm{Cs}$
$^{127}_{53}\mathrm{I}$
$^{131}_{54}\mathrm{Xe}$
$^{131}_{52}\mathrm{Te}$
Explanation
This question tests your ability to read and interpret nuclear equations that show how nuclei transform during fission, fusion, or radioactive decay, including identifying particles emitted and products formed. Nuclear equations use special notation where each nucleus or particle is written with its element symbol, mass number (superscript, total protons + neutrons), and sometimes atomic number (subscript, number of protons): for example, ²³⁸U represents uranium-238 with mass number 238 and atomic number 92 (uranium always has 92 protons). The equation shows what happens: ²³⁸U → ²³⁴Th + ⁴He means uranium-238 decays to thorium-234 (mass 234, atomic 90) plus an alpha particle (⁴He, which is a helium nucleus with mass 4, atomic 2). In nuclear equations, both mass numbers and atomic numbers are conserved (the sums on left equal sums on right): check 238 = 234 + 4 ✓ and 92 = 90 + 2 ✓. Common particles: alpha (⁴He), beta (⁰₋₁e, electron), neutron (¹n), proton (¹H). In beta decay, ¹³¹₅₃I → X + ⁰₋₁e, mass stays 131 (131= mass of X +0), atomic 53= Z of X + (-1) so Z=54, making X ¹³¹₅₄Xe. Choice B correctly interprets the nuclear equation by properly identifying the product nucleus as xenon-131. A distractor like choice A (¹³¹₅₂Te) fails because beta decay increases atomic number by 1, not decreases it—remember, beta turns a neutron to a proton, boosting Z. Reading nuclear equations step-by-step: (1) Identify what's on the left (reactant nucleus/nuclei) and right (product nucleus/nuclei and particles). (2) Check conservation: add mass numbers on left, add on right, should equal. Add atomic numbers on left, add on right, should equal. This tells you the equation is valid. (3) Identify unknowns: if you see X in equation, use conservation to find it. Example: ²²⁶Ra → ²²²Rn + X. Mass: 226 = 222 + ? → X has mass 4. Atomic: 88 = 86 + ? → X has atomic 2. So X is ⁴₂He (alpha particle). (4) Classify process: one splitting (fission), two combining (fusion), or one emitting particle (decay). The pattern reveals process type! Common particle recognition: if mass drops by 4 and atomic by 2 → alpha emitted (⁴He). If atomic number increases by 1 with no mass change → beta emitted (electron, ⁰₋₁e). If just gamma (energy), no mass or atomic change. If neutrons involved (¹n) and large nucleus splits → fission. If light nuclei combine → fusion. These patterns repeat across nuclear chemistry, so recognizing them once helps with all nuclear equations! Nuclear vs chemical equations: CHEMICAL equations balance atom counts using coefficients (2H2 + O2 → 2H2O keeps atoms same type, just rearranged). NUCLEAR equations balance mass and atomic numbers, but atoms actually CHANGE into different elements (uranium becomes thorium, carbon becomes nitrogen)—this is the key difference! Nuclear changes transform elements, chemical changes only rearrange them. Fantastic progress on products—stay encouraged!
In the fusion equation $$^{2}{1}\mathrm{H} + {}^{2}{1}\mathrm{H} \rightarrow {}^{3}{2}\mathrm{He} + {}^{1}{0}\mathrm{n},$$ which statement best describes what is happening?
A nucleus emits an alpha particle.
Two light nuclei combine to form a heavier nucleus.
A nucleus emits a beta particle and its mass number decreases by 4.
A heavy nucleus splits into two smaller nuclei.
Explanation
This question tests your ability to read and interpret nuclear equations that show how nuclei transform during fission, fusion, or radioactive decay, including identifying particles emitted and products formed. Nuclear equations use special notation where each nucleus or particle is written with its element symbol, mass number (superscript, total protons + neutrons), and sometimes atomic number (subscript, number of protons): for example, ²³⁸U represents uranium-238 with mass number 238 and atomic number 92 (uranium always has 92 protons). The equation shows what happens: ²³⁸U → ²³⁴Th + ⁴He means uranium-238 decays to thorium-234 (mass 234, atomic 90) plus an alpha particle (⁴He, which is a helium nucleus with mass 4, atomic 2). In nuclear equations, both mass numbers and atomic numbers are conserved (the sums on left equal sums on right): check 238 = 234 + 4 ✓ and 92 = 90 + 2 ✓. Common particles: alpha (⁴He), beta (⁰₋₁e, electron), neutron (¹n), proton (¹H). This fusion equation, ²₁H + ²₁H → ³₂He + ¹₀n, shows two light deuterium nuclei combining into a heavier helium-3 plus a neutron, with mass (4=3+1) and atomic (2=2+0) conserved. Choice C correctly interprets the nuclear equation by recognizing that two light nuclei combine to form a heavier nucleus, describing fusion. A distractor like choice A fails because it describes fission (splitting), but here nuclei are merging—note the number of reactants and products. Reading nuclear equations step-by-step: (1) Identify what's on the left (reactant nucleus/nuclei) and right (product nucleus/nuclei and particles). (2) Check conservation: add mass numbers on left, add on right, should equal. Add atomic numbers on left, add on right, should equal. This tells you the equation is valid. (3) Identify unknowns: if you see X in equation, use conservation to find it. Example: ²²⁶Ra → ²²²Rn + X. Mass: 226 = 222 + ? → X has mass 4. Atomic: 88 = 86 + ? → X has atomic 2. So X is ⁴₂He (alpha particle). (4) Classify process: one splitting (fission), two combining (fusion), or one emitting particle (decay). The pattern reveals process type! Common particle recognition: if mass drops by 4 and atomic by 2 → alpha emitted (⁴He). If atomic number increases by 1 with no mass change → beta emitted (electron, ⁰₋₁e). If just gamma (energy), no mass or atomic change. If neutrons involved (¹n) and large nucleus splits → fission. If light nuclei combine → fusion. These patterns repeat across nuclear chemistry, so recognizing them once helps with all nuclear equations! Nuclear vs chemical equations: CHEMICAL equations balance atom counts using coefficients (2H2 + O2 → 2H2O keeps atoms same type, just rearranged). NUCLEAR equations balance mass and atomic numbers, but atoms actually CHANGE into different elements (uranium becomes thorium, carbon becomes nitrogen)—this is the key difference! Nuclear changes transform elements, chemical changes only rearrange them. You're excelling at descriptions—keep shining!