Category: Part 6: Atomic & Nuclear

Problem Statement $^{14}$C is produced in the atmosphere by neutrons from cosmic rays: $n + ^{14}N \to ^{14}C + p$. If the production rate equals the decay rate, find the steady-state $^{14}$C/$^{12}$C ratio. ($T_{1/2}(^{14}C) = 5730$ yr; atmospheric $n$ flux $= 2$ n/cm²·s; $\sigma = 1.8$ b) Given Information All quantities, constants, and constraints stated…

Problem Statement Solve the quantum/modern physics problem: Solve the work-energy problem: A metastable state has lifetime $\tau = 1$ ms. Find the energy uncertainty and the minimum linewidth. $$\Delta E = \hbar/\tau = 1.055\times10^{-34}/10^{-3} = 1.055\times10^{-31} \text{ J} = 6.6\times10^{-13} \text{ eV}$$ $$\Delta\nu = \Delta E/h = 1/(2\pi\tau) = 159 \t Given Information Frequency $\nu$…

Problem Statement Solve the nuclear physics problem: Solve the work-energy problem: Define mass excess $\Delta = (M – A\cdot u)c^2$ and find it for $^{12}$C and $^{14}$N. Masses: $M(^{14}N) = 14.00307$ u. Mass excess: $\Delta = (M – A)\times931.5$ MeV (where $M$ is in atomic mass units and $A$ is the mass number) $^{12}$C: $M…

Problem Statement Explain the physical significance of the fine structure constant $\alpha = e^2/(4\pi\varepsilon_0\hbar c) \approx 1/137$. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation…

Problem Statement Explain the anomalous Zeeman effect. For the sodium D lines, how many components appear? Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation law…

Problem Statement In scanning tunneling microscopy (STM), the tip-sample distance changes by $\Delta d = 0.1$ nm. By what factor does the tunneling current change if $\kappa = 10^{10}$ m$^{-1}$? Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This…

Problem Statement Using the Born approximation, find the differential scattering cross section for a Yukawa potential $V = (V_0/r)e^{-r/a}$. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify…

Problem Statement For the $n=2$ states of hydrogen in an electric field $\mathcal{E}$, find the first-order energy shifts (linear Stark effect). Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is…

Problem Statement Solve the nuclear physics problem: Solve the nuclear physics problem: Explain the concept of isospin in nuclear physics. Find the isospin of the deuteron and the nucleon. Isospin (isobaric spin): Since the nuclear force is charge-independent, protons and neutrons are treated as two states of a single particle — the nucleon — with…

Problem Statement Using the matrix element $\langle f|\mathbf{r}|i\rangle$, derive the electric dipole selection rules $\Delta l = \pm1$, $\Delta m_l = 0, \pm1$. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The…