Category: Part 6: Atomic & Nuclear

Problem Statement Derive Wien’s displacement law from Planck’s formula and find the peak wavelength for the Sun ($T = 5778$ K). 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 Write the Bose-Einstein distribution for photons and derive the Planck black-body radiation formula. 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 or…

Problem Statement Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: Write the Fermi-Dirac distribution and find the Fermi energy for free electrons in a metal with $n = 8.5\times10^{28}$ m$^{-3}$ (copper). Fermi-Dirac distribution: $$f(E) = \frac{1}{e^{(E-E_F)/(k_BT)} + 1}$$ At $T=0$: $f=1$ for $E E_F$. The Fermi energy: $$E Given Information Frequency $\nu$ or…

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 A proton annihilates with an antiproton at rest. What are the possible products and their energies? 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…

Problem Statement Solve the nuclear physics problem: From the liquid drop model, derive the condition for spontaneous fission. All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) This problem draws on fundamental physical principles. The key is to identify which conservation l Given Information Nuclide symbol,…

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 Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: An electron is confined to a cubical quantum dot of side $L = 10$ nm. Find the ground state energy and the first excitation energy. A cubic quantum dot is a 3D infinite square well. Energy levels: $$E_{n_x,n_y,n_z} = \frac{\pi^2\hbar^2}{2m_eL^2}(n_x^2+n_y^2+ Given Information Frequency…

Problem Statement Solve the nuclear physics problem: Solve the optics problem: Mirror nuclei $^7$Li and $^7$Be differ only by swapping one proton and one neutron. Their mass difference is 1.644 MeV. Find the Coulomb energy difference and verify charge independence. Mirror nuclei: $^7_3$Li (3p, 4n) and $^7_4$Be (4p, 3n). They differ by one $p\leftright Given…

Problem Statement For a 3s electron in Na ($Z=11$), estimate the effective nuclear charge using Slater’s rules. 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…