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AP Intermediate 2nd Year Atoms and Nuclei — practice questions

Explore 82 free Atoms and Nuclei questions in AP Intermediate 2nd Year Physics. Open each question or exercise to read its content, reference answers and available explanation.

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Atoms and Nuclei questions and exercises with answers

Showing questions 1–30 of 82.

Bohr's quantisation condition for the angular momentum $L$ of an electron in the $n^\text{th}$ orbit isRead the answer and worked solution →The ratio of the first excitation energy of a hydrogen atom ($E_2 - E_1$) to its ionisation energy from the ground state isRead the answer and worked solution →The unified atomic mass unit (u) is defined as exactly $1/12$ of the mass of an atom of which isotope?Read the answer and worked solution →The mass defect $\Delta m$ of a nucleus $\,^{A}_{Z}\mathrm{X}$ with mass $M$ is defined asRead the answer and worked solution →The energy equivalent of one unified atomic mass unit (1 u) is closest toRead the answer and worked solution →When a nucleus $\,^{A}_{Z}\mathrm{X}$ undergoes ALPHA decay, the daughter nucleus hasRead the answer and worked solution →In BETA-MINUS ($\beta^-$) decay, the parent nucleus emits an electron AND another particle. The other particle isRead the answer and worked solution →A radioactive sample has half-life $T_{1/2} = 5$ years. Starting with $N_0$ undecayed nuclei, the number remaining after $20$ years isRead the answer and worked solution →The total binding energy of $\,^{16}_{8}\mathrm{O}$ is approximately $127.6\,\text{MeV}$. Its binding energy per nucleon is closest toRead the answer and worked solution →NEET · Physics · Bohr's Atom — Gap FillRead the answer and worked solution →NEET · Physics · Fission or FusionRead the answer and worked solution →NEET · Physics · Bohr-Atom Transitions — Energy OrderRead the answer and worked solution →Line up three jumps in one bandRead the answer and worked solution →Order the atomic models in this chapterRead the answer and worked solution →True or false: Rutherford's two difficultiesRead the answer and worked solution →Which model does this belong to?Read the answer and worked solution →Complete Bohr's first postulateRead the answer and worked solution →True or false: line spectraRead the answer and worked solution →Charge and neutralityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Tap every problem Bohr's model was built to solveRead the answer and worked solution →Flip and pair: model with its pictureRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Strength or weakness?Read the answer and worked solution →Complete the size of the nucleusRead the answer and worked solution →Reading the models backRead the answer and worked solution →Bohr's postulatesRead the answer and worked solution →Explained, or left unexplained?Read the answer and worked solution →

Worked practice questions

Bohr's quantisation condition for the angular momentum $L$ of an electron in the $n^\text{th}$ orbit is

  1. $L = n\hbar$ where $\hbar = h$
  2. $L = \dfrac{nh}{2\pi}$
  3. $L = \dfrac{n^2 h}{2\pi}$
  4. $L = \dfrac{h}{2\pi n}$
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Correct answer: B. $L = \dfrac{nh}{2\pi}$

1. Your syllabus: the angular momentum of an electron in a stable orbit is an integral multiple of $h/2\pi$. 2. Writing this as a formula: $L = \dfrac{nh}{2\pi}$ where $n = 1, 2, 3, \ldots$ is the principal quantum number. 3. Using the reduced Planck constant $\hbar = h/2\pi$, this can also be written $L = n\hbar$. 4. Option A defines $\hbar = h$, which is WRONG ($\hbar = h/2\pi$, off by a factor of $2\pi$). Option C has an extra factor of $n$. Option D inverts the dependence ($1/n$ instead of $n$). 5. This quantisation is what FORCES the discrete orbits and energies of the hydrogen atom de Broglie later showed it follows from the standing-wave requirement $2\pi r_n = n\lambda$. _Source: syllabus Physics Part 2, Ch 12, §12.4 (Bohr's second postulate, Eq. 12.5) + §12.6, p. 9 + p. 11–12._

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The ratio of the first excitation energy of a hydrogen atom ($E_2 - E_1$) to its ionisation energy from the ground state is

  1. $3 : 4$
  2. $1 : 4$
  3. $3 : 1$
  4. $1 : 16$
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Correct answer: A. $3 : 4$

1. Use $E_n = -13.6/n^2\,\text{eV}$. 2. Ionisation energy from the ground state: $E_\infty - E_1 = 0 - (-13.6) = 13.6\,\text{eV}$. 3. First excitation energy: $E_2 - E_1 = -3.40 - (-13.6) = 10.20\,\text{eV}$. 4. Ratio: $\dfrac{10.20}{13.60} = \dfrac{10.2}{13.6}$. Multiply numerator and denominator by 10: $\dfrac{102}{136} = \dfrac{3}{4}$. 5. So $(E_2 - E_1) : E_\text{ion} = 3 : 4$. 6. Algebraic shortcut: ratio = $\dfrac{(1/1^2) - (1/2^2)}{(1/1^2) - 0} = 1 - \dfrac{1}{4} = \dfrac{3}{4}$. 7. Other options come from computing the wrong difference or comparing $E_2$ to $E_1$ directly. _Source: syllabus Physics Part 2, Ch 12, §12.4.1, p. 10 (worked values $E_1 = -13.6$, $E_2 = -3.4$, excitation energy $= 10.2\,\text{eV}$)._

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The unified atomic mass unit (u) is defined as exactly $1/12$ of the mass of an atom of which isotope?

  1. $\,^{1}_{1}\mathrm{H}$
  2. $\,^{12}_{6}\mathrm{C}$
  3. $\,^{16}_{8}\mathrm{O}$
  4. $\,^{14}_{7}\mathrm{N}$
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Correct answer: B. $\,^{12}_{6}\mathrm{C}$

1. syllabus defines the unified atomic mass unit by international convention. 2. The reference standard is the neutral atom of carbon-12, $\,^{12}_{6}\mathrm{C}$, in its electronic ground state. 3. One unified atomic mass unit: $1\,u = \dfrac{1}{12}\,m(\,^{12}_{6}\mathrm{C}) = 1.66054\times 10^{-27}\,\text{kg}$. 4. Carbon-12 was chosen in 1961 because it gives integer-friendly mass values for most elements. 5. Options A, C, D were never the standard — though older systems (pre-1961) used $\,^{16}\mathrm{O}$ for chemistry (option C), this gave a slightly different unit than physics's $\,^{16}\mathrm{O}$ isotope-only definition. _Source: syllabus Physics Part 2, Ch 13 "Nuclei", §13.2 (Atomic Masses), p. 1._

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